Question : Simplify the following expression.
$\frac{x^2-2 x-63}{x^2+14 x+49}$
Option 1: $\frac{x+9}{x+7}$
Option 2: $\frac{x-7}{x+7}$
Option 3: $\frac{x+7}{x-7}$
Option 4: $\frac{x-9}{x+7}$
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Correct Answer: $\frac{x-9}{x+7}$
Solution :
Given:
$\frac{x^2-2 x-63}{x^2+14 x+49}$
= $\frac{(x^2-2 x+1)-64}{x^2+2×x×7+7^2}$
= $\frac{(x-1)^2-8^2}{(x+7)^2}$
= $\frac{(x+7)(x-9)}{(x+7)^2}$
= $\frac{(x-9)}{(x+7)}$
Hence, the correct answer is $\frac{(x-9)}{(x+7)}$.
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