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

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

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

simplify

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

\frac{2}{x - 1}

Solution steps

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

Cancel

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

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

Apply the fraction rule:

a + \frac{b}{c} = \frac{a c + b}{c}

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

Apply rule:

1 \cdot a = a

- 1 \cdot (x - 1) = - (x - 1)

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

Simplify

- (x - 1) + x + 1 : 2

= \frac{2}{x - 1}

12 \cdot (- 3)

\frac{1}{1} + \frac{2}{3}

2 \frac{1}{12}

i (3 + 4 i)^{2}

2 (1 - i)^{2} + 3 (- 2 + 4 i) - 5 (3 - 2 i)^{2}