Question

Evaluate: $\frac{a^2-4a+4}{-a^2+2a+15}\times \frac{a^2-9}{(a-2{)}^2}$

• A. $\frac{a+3}{a-5}$
• B. $\frac{a-3}{a-5}$
• C. $\frac{a-3}{a-2}$
• D. $\frac{a-5}{a-2}$

Answer 1

The correct option is B $\frac{a-3}{a-5}$

Factor of $a^2-4a+4=(a-2)(a-2)=(a-2{)}^2$
Factor of $-a^2+2a+15=(a+3)(a-5)$
$a^2-b^2=(a+b)(a-b)$, $(a^2-3^2)=(a+3)(a-3)$
So, $\frac{(a-2{)}^2}{(a+3)(a-5)}\times \frac{(a+3)(a-3)}{(a-2{)}^2}$
$=$ $\frac{a-3}{a-5}$