find all the possible of x for which of the below is true:

[tex] \frac{2x}{x + 3} + \frac{3}{x - 3} = \frac{8}{x^{2} - 9 } [/tex]

Answers

Answer 1

Answer:

x = [tex]\frac{1}{2}[/tex] , x = 1

Step-by-step explanation:

Given

[tex]\frac{2x}{x+3}[/tex] + [tex]\frac{3}{x-3}[/tex] = [tex]\frac{8}{x^2-9}[/tex] ← denominator is a difference of squares

[tex]\frac{2x}{x+3}[/tex] + [tex]\frac{3}{x-3}[/tex] = [tex]\frac{8}{(x+3)(x-3)}[/tex]

Multiply through by (x + 3)(x - 3) to clear the fractions

2x(x - 3) + 3(x + 3) = 8 ← distribute left side and simplify

2x² - 6x + 3x + 9 = 8

2x² - 3x + 9 = 8 ( subtract 8 from both sides )

2x² - 3x + 1 = 0 ← in standard form

(2x - 1)(x - 1) = 0 ← in factored form

Equate each factor to zero and solve for x

2x - 1 = 0 ⇒ 2x = 1 ⇒ x = [tex]\frac{1}{2}[/tex]

x - 1 = 0 ⇒ x = 1


Related Questions

Roll needs to make a sauce mixture of 2/5 sand and 2/5 of clay and one for Pete Mas to put his plants yes 75 pounds of sand how many total pounds of soil rather have it he adds clay and Pete Moss to the sand to make the correction mixture

Answers

Answer:

187.5 pounds

Step-by-step explanation:

Fraction of sand = 2/5

Fraction of clay = 2/5

Fraction of peat = 1/5

Pounds of sand = 75

The total pounds of soil required to make Correct mixture : let that be x

Hence,

Using the sand Fraction and pounds which we know :

2/5 of x = 75

2x / 5 = 75

Cross multiply :

2x = 75 * 5

2x = 375

x = 375 / 2

x = 187.5

Required pond of sand =187.5 pounds

What is the area of a circle with a diameter of 18.2 cm?

Use 3.14 for ∏ and round your final answer to the nearest hundredth.

The area is ___ square cm.

Answers

Answer:

260.02 cm²

Step-by-step explanation:

radius of circle= 18.2÷2

=9.1

area of circle= πr²

= 3.14×9.1²

= 260.02 cm² (nearest hundredth)

Answer:

Solution given:

diameter=18.2cm

[r]radius=diameter /2=18.2/2=9.1cm

Now

Area of circle=πr²=3.14*(9.1)²=260.02cm²

The area is _260__ square cm.

MATH PLEASE HELP ! PLEASE

Answers

Answer:

wait I am solving this

Step-by-step explanation:

mark it as the brainliest to get the answer

If 4x - 8 = 4 , find the value of x​

Answers

Answer:

x=3

Step-by-step explanation:

4x-8=4

4x=12

4x/4=12/4

x=3

Answer:

x = 3

Step-by-step explanation:

Add 8 to both sides.

4x = 4 + 8

Simplify 4 + 8 to 12.

4x = 12

Divide both sides by 4.

x = 12 ÷ 4

Simplify 12 ÷ 4 to 3

x = 3

HELP ME . Help me please

Answers

Answer:

Top right corner

Step-by-step explanation:

Write the equation x+5y=5 in slope intercept form.

Answers

Answer:

y=-1/5+1

(negative one over 5)

Step-by-step explanation:


Which is closest to the height of the building?
(Round to nearest tenth

Answers

Answer:

[tex]let \: it \: be \: x \\ \cos(70 \degree) = \frac{12}{x} \\ x = \frac{12}{ \cos(70 \degree) } \\ x = 35.1 \: ft[/tex]

[tex]height = \sqrt{ {35.1}^{2} - {12}^{2} } \\ = \sqrt{1088.01} \\ = 33.0 \: ft[/tex]

Emily earns $15 for each car she washes. Create an equation to represent the relationship between the numbers of cars washed c, and the amount, in dollars,Emily earns,m. HELP!!

Answers

Answer:Im not sure but btw the state test just is on how your teacher teach you and the school if u do bad it affects the school but don’t purposely not try this is what i put for the answer

Step-by-step explanation:10c 15m hopw it helps!

The total cost of a gym membership, C, in Australian dollars (AUD), in John's Gym can be modelled by the function C = 65t+30, where t is the time in months. Calculate the gym membership cost over 12 month duration

Answers

Answer:

810 AUD

Step-by-step explanation:

t is time in months: you have to substitute with the number of months given from the question.

C=65t + 30 ==> substitute t with 12 since the question provided you the number of months.

--> C = 65(12) + 30 = 780 + 30 = 810

it is an math question i am doing my paper i need help 7 class question
factorize: a²-100​

Answers

Answer: (a + 10)(a - 10)

If - 2x + 3 = 7 and 3x + 1 = 5+ y, the value of y is

Answers

Answer:

The value for x is -2 and the value for y is -10 .

Step-by-step explanation:

Firstly , let's write the equations

              -2x+3=7      (   equation 1 )               3x+1 =5+y    (equation 2 )

 

solving equation 1 to get the values of x

          or ,    -2x+3=7          

      or,  -2x+3-3 =7-3 (subtracting -3 on both sides )

       or ,  -2x=4

        or,  -2x/2  =   4/2  (dividing  by two on both sides )

         or ,  -x =2

           or  x = -2

now let's substitute the values of x  in the equation 2

           3x+1 =5+y (writing second equation as it is )

           or, 3x+1-1=5+y-1 (subtracting  -1 on both sides )

            or , 3x = 4+y  

              or , 3 × -2 = 4+y  (substituting the values of x from equation 1 )

                or ,  -6  =  4 +y

                   or ,  -6-4 = 4+y-4 ( subtracting -4 on both sides  )

                     or ,    -10 = y

      Therefore the values of x and y is -2 and  -10 respectively .

                Hope it helped you .  If you find the answer useful  please rate brainliest , If not Thanks anyway .

 

Can someone help me out, I will give out brainly.

Answers

Answer:

370

Step-by-step explanation:

Area of the entire thing is 20*20 = 400

You need to remove the triangle since it's not shaded, so find the area of the triangle and subtract it from the total (total = 400)

Area of triangle:

First find the height using pythagorean theorem

5*12 = 156

Then divide by two: 60/2= 30

400-30 = 370

3 x 4 x 25 x c = ?
c = 16

Answers

Answer:

4800

Step-by-step explanation:

If c = 16, the equation is:

3 * 4 * 25 * 16 = 4800

Someone pls help me!!!!

Answers

Answer:

J)  2r⁴s⁴

Step-by-step explanation:

if you know the area and the base, you can divide them to find the height

16r⁸s⁶ ÷ 8r⁴s² = 2r⁴s⁴

HELP ME PLEASE


Explain to Raven what she did correctly in the first two problems that she did not do in the last problem, and how to correct her mistake

Answers

Answer:

She changed the symbols in the first two problems because they were divided by a negative number whereas she shouldn't have changed the symbol in the last problem as it was not divided by a negative number and so the sign remains the same.

If−3x − 7 = 23, then 6x =_____?

Answers

Answer:

22

Step-by-step explanation:

We will first find the value of x .

Then we will multiply 6 to the value of x

As a contestant on a televised game show, Kiara gets to spin the big prize wheel, which has a radius of 2 meters. What is the prize wheel's area

Answers

Answer:

12.57

Step-by-step explanation:

We need to find of area of a circle and the formula for that is pie * radius ^2.

Pie * 2 squared = 12.57 rounded to the nearest hundredth

What is the sum of the interior angles of the polygon shown below?

Answers

Answer:

540°

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

Here n = 5 , then

sum = 180° × 3 = 540°

The answer would be 540 if it’s correct let me know!

someone help me it's due today

Answers

Answer:

y=2x+6

Step-by-step explanation:

y=2x+6 you are welcome!!

what is the speed of a bus that travels 350km in 5 hours

Answers

Answer:

We need to make it a unit rate.

350/5

70/1

70km per 1 hour

Answer:

70km

Step-by-step explanation:

350÷5 =70

Can you help me with this

Answers

Answer:

3 and 4

Step-by-step explanation:

The length of a rectangle is 10x² – 13x - 3 / 4x + 3 and the width is 4x² + 11x + 6 / 2x - 3 inches. Find the area of the rectangle.​

Answers

Answer:

use this formula ot find area of rectangl 2l +2w

If a car can travel 250 miles on 10 gallons of fuel , how many gallons are requiered to travel 1325 miles

Answers

Answer:

53 gallons of fuel

Step-by-step explanation:

Step 1: Set up a fraction given the data (Let "x" represent the distance in miles.)

[tex]\frac{10}{250} = \frac{x}{1325}[/tex]

Step 2: Divide the given values (The given values are 10 over 250. We are doing this because we need to know the difference between those two figures.) (Trick: For this case, all you need to do is cancel both zeros and the answer is 0.04 once divided)

[tex]\frac{10}{250}\\\\10 \div 250\\\\= 0.04[/tex]

Step 3: Multiply the result to the last value (Since we've found the difference between them by division, we will have to do the opposite operation in order to find the answer.)

[tex]1325 \times 0.04\\\\= 53[/tex]

Therefore, 53 is the amount of gallons of fuel needed.

The shoes you want to buy are on sale for 25% off the original price is $75 what is the sale price of the shoes

Answers

Answer:   $56.25

Step-by-step explanation:

25  as a decimal is 0.25

So you multiply  0.25  * 75 = 18.75

75 - 18.75 = 56.25

The sale price  of the shoe is  $56.25.

what is the solution 6x-4 =2(3x-2)

Answers

Answer:

x= 0

Step-by-step explanation:

6x-4=2(3x-2)

or,6x-4=6x-4

or,x=o

There are infinite solution of the expression.

We have to given that,

An expression to solve,

6x - 4 = 2 (3x - 2)

Now, We can simplify as,

6x - 4 = 2 (3x - 2)

Apply distributive property,

6x - 4 = 6x - 4

Combine like terms,

6x - 6x = 4 - 4

0 = 0

Hence, There are infinite solution of the expression.

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ6

the five classes at steam elementary are going to the zoo. the teacher need to put the students in group of tens the number of students in each class is shown​

Answers

there will be 13 groups with 4 leftover

Step-by-step explanation:

1)Add all the elementary learners

2) devide the answer you get from step 1 by 10.

3)the whole number will be number of learners in each group and the remainder will be the remaining learners

74,308 Problem: Round the number above to the nearest ten.

Answers

Answer:

74,310

Hope this helped! ^^

Answer:

[tex] = 74,310[/tex]

step by step explanation:

can someone please help​

Answers

About what you dont write anything

Answer:

for A

the law

V=Bh or V=πr2h

I will use this V=Bh

V= 16·21

V= 336cm³

For E

the law

A= 1/2·(A + B)·H

A= 1/2·(14 + 8)·4

A= 44cm²

V= A·H

V= 44·4

V= 176 cm³

make a search for each one :

B. triangular prism volume calculator

C. pyramid prism volume calculator

D. rectangular prism volume calculator

F. cube volume calculator

Can someone explain how to do this? I keep getting it wrong

Answers

Answer:

Step-by-step explanation:

in order to find the measurements of all the angles you must find x and to find x you have to realize that the total sum of a triangle inner angles is 180 so you add all those together (48+x+x-44=180) and then if you solve that it gives you 2x+4=180 and then simplify 2x=176 and then x=88

then you plug x into the angles in order to find out the actual measurements

so a is obviously 48 but then b is equal to x which isequal to 88

and then for c it will be x-44 so its 88-44 which equals 44 and that is your answer

if you want to double check take all of your answers and see if they add up to 180

The figure is made of 2 right rectangular prisms.
3 ft
3 ft
7 ft
14 ft
3 ft
12 ft
Which expression can be used to find the volume of the figure in cubic feet?
O A. 7x3 x 12
OB. 7 x 6 x 12
OC. (7+3+3) + (12+3+4)
OD. (7X 3 3) + (12 X 3 X 4)
O E. (7x 3 x 3) + (9 x3 4)

Answers

Answer:

E

Step-by-step explanation:

I took the MAP Test.

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