First slide

Theory of expressions

Question

If $a^{2} - 4 a + 1 = 4$ ,then the value of $\frac{a^{3} - a^{2} + a - 1}{a^{2} - 1} (a^{2} \neq 1)$ is equal to____.

Moderate

Solution

Given,
$a^{2} - 4 a + 1 = 4 \Rightarrow a^{2} + 1 = 4 (1 + a)$
$y = \frac{(a - 1) (1 + a^{2})}{a^{2} - 1} = \frac{a^{2} + 1}{a + 1} = \frac{4 (a + 1)}{a + 1} = 4$

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