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Quantitative Aptitude

Solving Inequalities

Solve: 5 x-6+...

Question

Solve: $\frac{(5 x - 6 + x^{2})}{(x - 1)}$

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Solution

The expression is $\frac{(5 x - 6 + x^{2})}{(x - 1)}$
Take the numerator and factorise it:
$x^{2} + 5 x - 6 = x^{2} + 6 x - x - 6 = x (x + 6) - 1 (x + 6) = (x + 6) (x - 1)$
So, the expression becomes $= \frac{(x + 6) (x - 1)}{(x - 1)}$
$= x + 6$

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