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

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

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

simplify

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

\frac{x + 1}{x}

Solution steps

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

Join

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

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

Join

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

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

Apply the fraction rule:

\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a \cdot d}{b \cdot c}

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

Cancel

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

= \frac{x + 1}{x}

x^{2} (x^{2} + 4)

8 (54 - 69)

0.19

0.56

x^{2} + 12 x - 28

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