Using the identity $a^2 - b^2 = (a+b)(a-b)$, simplify $\frac{x^2 - 9}{…

Question

Using the identity $a^2 - b^2 = (a+b)(a-b)$, simplify $\frac{x^2 - 9}{4x - 12}$ for $x 
eq 3$.

Accepted Answer

D. $\frac{x + 3}{4}$

Factor numerator with the difference of squares: $x^2 - 9 = (x+3)(x-3)$. Factor denominator: $4x - 12 = 4(x - 3)$. Cancel the shared factor $(x-3)$ for $x 
eq 3$, leaving $(x+3)/4$. Option A drops the wrong factor; option C inverts numerator and denominator.

Answer

$\frac{x - 3}{4}$

Answer

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

Answer

$\frac{4}{x + 3}$

Using the identity $a^2 - b^2 = (a+b)(a-b)$, simplify $\frac{x^2 - 9}{4x - 12}$ for $x \neq 3$.