Solve for x (x+2)/(x^2-4)=1/2

$\frac{x + 2}{x^{2} - 4} = \frac{1}{2}$

Simplify both sides.

Simplify the denominator.

Rewrite $4$ as $2^{2}$ .

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

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 2$ .

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

Cancel the common factor of $x + 2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.

$1 \cdot 2 = (x - 2) \cdot 1$

Solve the equation for $x$ .

Rewrite the equation as $(x - 2) \cdot 1 = 1 \cdot 2$ .

$(x - 2) \cdot 1 = 1 \cdot 2$

Multiply $x - 2$ by $1$ .

$x - 2 = 1 \cdot 2$

Multiply $2$ by $1$ .

$x - 2 = 2$

Move all terms not containing $x$ to the right side of the equation.

Add $2$ to both sides of the equation.

$x = 2 + 2$

Add $2$ and $2$ .

$x = 4$

Solve for x (x+2)/(x^2-4)=1/2

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