# Math

posted by April

Solve for x.

x/(x-2) + (2x)/[4-(x^2)] = 5/(x+2)

1. Steve

putting everything over a common denominator of (x-2)(x+2), we have

x^2 = 5(x-2)
x^2 - 5x + 10 = 0
then just solve that for x

Make sure that x ≠ ±2 since those values are not allowed in the original equation

2. MathMate

x/(x-2) + (2x)/[4-(x^2)] = 5/(x+2)

This calls for finding the common denominator, and then solving for x using the numerators.
Do not forget to exclude the asymptotes values of x where the denominator becomes zero.

LCM (lowest ommon multiple) of denominators (x-2), (4-x²) and (x+2) is (x²-4), since (x-2)(x+2)=(4-x²)

Provided that x≠2 and x≠-2, then we can write the equation above as:

[x(x+2)-2x]/(x²-4) = 5(x-2)/(x²-4)
provided x≠2 and x≠-2

Equating numerators,
x²+2x-2x=5(x-2)
=>
x²-5x+10=0

However, the solution does not have real roots. The complex roots are:
x=(5±√*i)/2

3. MathMate

x=(5±(√15)*i)/2

If you do not expect complex roots, please check for typos in the original question.

4. April

Thank you guys! That is what I got. I wasn't expecting the complex roots.. That's why I wanted to check whether or not I was doing it right!

5. MathMate

You're welcome!

## Similar Questions

1. ### math

Can someone please help me with this math problem. My teacher is looking for me to show my work, but I don't how to solve the problem to show my work. Please help!!! The problem is 2 1/2 + 3 1/4 + 3 5/8. Thank you for your help.
2. ### mat115

Please help me with this math question. I am asked to show my work but I don't know how to solve the problem to show my work. The question is: Choose the correct list of factors of the number 8. Again, I have to show my work with this …
3. ### math

solve: 4+8 1/2 -:- (1/4) to the third power. solve -11-(x+30)=-41-2 (5x-18) please show your work
4. ### math

2. Simplify. Please be sure to show all of your work. -3(-9) – |-5 – 3 3. Simplify. Please show all of your work 9c^3+7c-(3c^3-12+c) 4. Solve 4x- 3(5x-8) =23-9(x+2) . Please show all of your work 5. Solve the following equation …
5. ### prealgebra

can you please help me and help me solve this and show work: Identify the percent of change as an increase or a decrease. Then find the percent of change. #1.) Original:45 New:30 Please help i don't understand how to solve and show …
6. ### Math..solve for u

Solve u-2[2=3 [ is square root. Please show work
7. ### math. solve for t

1/1024=42*0.5^(t/12.5) Solve for t. Please show work. Much appreciated!
8. ### Math

6x-4y=54 -9x+2y=-69 Which system would work best to solve?