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

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

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

simplify

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

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

Solution steps

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

Factor

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

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

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}

\frac{1}{2} - \frac{5}{7}

8 + (- 11)

15 x + 2 x^{2} - x^{3}

- (3 x^{2} + 2 x) + (1 - 5 x)

(2 x^{2} + 5 x + 3) (x^{2} - 2 x + 1)