SOLUTION: Please solve: 2/2-x + 3/x+2 = 2x/x^2

SOLUTION: Please solve: 2/2-x + 3/x+2 = 2x/x^2 - 4 Thanks in advance!

Question 124742: Please solve:

2/2-x + 3/x+2 = 2x/x^2 - 4

Thanks in advance!
Answer by dolly(163) (Show Source): You can put this solution on YOUR website!
2/2-x + 3/x+2 = 2x/x^2 - 4
This can be re written as :
3/x+2 + 2/2-x = 2x/x^2 - 4
==> 3/x+2 - 2/x-2 = 2x/x^2 - 4 [the denominator is written as x-2 with a negative sign]
Taking the common denominator for the left side we get it as (x+2)(x-2)
Thus [3(x-2)- 2(x+2)] / (x+2)(x-2) = 2x / (x^2 - 4)
==> [3x - 6 - 2x - 4] / (x^2 - 4) = 2x / (x^2 - 4)[as (x+2)(x-2)= (x^2 - 4) ]
==> [3x - 6 - 2x - 4] = 2x [ multiplying both the sides by the denominator]
==> x - 10 = 2x
==> x - 2x = 10 [ adding - 2x + 10 to both sides]
==> - x = 10
==> x = - 10
good luck!!!

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