What is (x^2-1)/((x-1)^2) ?

The solution to (x^2-1)/((x-1)^2) is (x+1)/(x-1)

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simplify (x^2-1)/((x-1)^2)

simplify

\frac{x ^{2} - 1}{( x - 1 ) ^{2}}

\frac{x + 1}{x - 1}

Solution steps

\frac{x ^{2} - 1}{( x - 1 ) ^{2}}

Factor

x^{2} - 1 : (x + 1) (x - 1)

= \frac{( x + 1 ) ( x - 1 )}{( x - 1 ) ^{2}}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

(x - 1)^{2} = (x - 1) (x - 1)

= \frac{( x + 1 ) ( x - 1 )}{( x - 1 ) ( x - 1 )}

Cancel the common factor:

x - 1

= \frac{x + 1}{x - 1}

- 7 + 11

- 9 + 13

4 (x + 2)^{2}

2 (x - 2) + 5 x

15 + 6