Question

solve for x.
\\(\frac{1}{x - 2} - \frac{5}{x + 2} = \frac{8}{x^2 - 4}\\)
if there is more than one solution, separate them with commas.
if there is no solution, click on
o solution\.
x =
no solution √□ \\(\frac{□}{□}\\)
□,□,...

Explanation:

Step1: Factor denominator on right

Notice that $x^2-4=(x-2)(x+2)$.

Step2: Multiply by common denominator

Multiply all terms by $(x-2)(x+2)$ to eliminate fractions:
$$1(x+2) - 5(x-2) = 8$$

Step3: Expand and simplify left side

$$x+2 -5x +10 = 8$$
$$-4x +12 = 8$$

Step4: Isolate the variable term

Subtract 12 from both sides:
$$-4x = 8 - 12$$
$$-4x = -4$$

Step5: Solve for x

Divide both sides by -4:
$$x = \frac{-4}{-4} = 1$$

Step6: Check for extraneous solutions

Substitute $x=1$ into original equation:
$\frac{1}{1-2}-\frac{5}{1+2} = -1 - \frac{5}{3} = -\frac{8}{3}$, and $\frac{8}{1^2-4}=\frac{8}{-3}=-\frac{8}{3}$. Also, $x=1$ does not make any original denominator zero.

Answer:

$x=1$