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

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

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

simplify

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

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

Solution steps

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

Factor

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

= \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{\frac{x - 9}{x ^{3}}}{\frac{x ^{2} - 81}{x ^{2} + 8 x - 9}}

- 6 + 12

\frac{35}{10}

9 \div \frac{1}{3}

(- 4 - 8 i) - (- 6 + 9 i)