Question : Find the value of the expression $\frac{x^2-1}{x-1}-\frac{x^2-9}{x-3}$.
Option 1: 1
Option 2: –2
Option 3: –1
Option 4: 2
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Correct Answer: –2
Solution :
$\frac{x^2-1}{x-1}-\frac{x^2-9}{x-3}$
= $\frac{(x-1)(x+1)}{x-1}-\frac{(x-3)(x+3)}{x-3}$
= $(x+1) - (x+3)$
= $-2$
Hence, the correct answer is –2.
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