Question

Solve for x. 2/x^2−4 − 1/x+2=3/x−2 −32 −12 23 2

Answer 1

Answer:

$-\frac{1}{2}$

Step-by-step explanation:

1. Multiply both sides of the equation by the LCM (x - 2)(x + 2):

$\frac{2}{x^{2} -4} (x-2)(x+2)$

factor x² - 4 by rewriting it as x² - 2²

x² - 2² = (x + 2)(x - 2)

now we have;

$\frac{2}{(x+2)(x-2)} (x-2)(x+2)$

cancel the common factors (x - 2)(x + 2)

= 2

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$\frac{-1}{x+2} (x-2)(x+2)$

cross cancel the common factor (x + 2)

$\frac{-1}{x-2}=-(x-2)=-x+2$

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$\frac{3}{x-2} (x-2)(x+2)$

cross cancel the common factor (x - 2)

3(x + 2)

distribute the 3

3x + 6

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combining all new values, we have;

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

-x + 4 = 3x + 6

2. Isolate x:

-x + 4-4 = 3x + 6-4

-x = 3x + 2

-x-3x = 3x-3x + 2

-4x = 2

-4x/-4 = 2/-4

x = $-\frac{1}{2}$

hope this helps!

Answer 2

Answer:

x = -1/2.

Step-by-step explanation:

x^2 - 4 = (x - 2)(x + 2)  so if we multiply each term by x^2 -4 we get:

2 - 1(x - 2) = 3(x + 2)

2 - x + 2 = 3x + 6

2 + 2 - 6 = 3x + x

4x = -2

x = -1/2.