Solve the Rational Equation for x (x^2-4)/(x-2)=2

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

Step 1

Factor each term.

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

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

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 $b = 2$ .

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

Reduce the expression by cancelling the common factors.

Reduce the expression $\frac{(x + 2) (x - 2)}{x - 2}$ by cancelling the common factors.

Cancel the common factor.

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

Rewrite the expression.

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

Divide $x + 2$ by $1$ .

$x + 2 = 2$

Step 2

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

Subtract $2$ from both sides of the equation.

$x = 2 - 2$

Subtract $2$ from $2$ .

$x = 0$