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(x^(2)-1)/(x^(2)-5x+4)

$\frac{x^{2}-1}{x^{2}-5 x+4}$

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Evaluate integers raised to rational exponents

Full solution

Q.

\frac{x^{2}-1}{x^{2}-5 x+4}

Factor Numerator and Denominator: Factor the numerator and the denominator. $\newline$ The numerator $x^2 - 1$ is a difference of squares and can be factored as $(x + 1)(x - 1)$ . $\newline$ The denominator $x^2 - 5x + 4$ can be factored by finding two numbers that multiply to $4$ and add up to $-5$ . These numbers are $-4$ and $-1$ , so the denominator factors as $(x - 4)(x - 1)$ .
Write Factored Form: Write the factored form of the expression. $\newline$ The expression becomes: $\newline$ $\frac{(x + 1)(x - 1)}{(x - 4)(x - 1)}$
Cancel Common Factors: Cancel out the common factors. $\newline$ The $(x - 1)$ term is present in both the numerator and the denominator, so we can cancel it out. $\newline$ The simplified expression is: $\newline$ $(x + 1) / (x - 4)$

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