Question

Rational algebraic expression x²-16/x²+8x+16

Answer 1

(x - 4)/(x + 4)

Step-by-step explanation:

$\begin{aligned}\tt\frac{x^2-16}{x^2+8x+16}&=\tt\frac{x^2-4^2}{\left(x+4\right)^2}\\&=\tt\frac{\left(x+4\right)\left(x-4\right)}{\left(x+4\right)^2}\\&=\tt\frac{x-4}{x+4}\end{aligned}$

Note :

• a² - b² = (a + b)(a - b)
• (a + b)² = a² + 2ab + b²