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

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

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

simplify

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

\frac{x + 1}{x}

Solution steps

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

Join

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

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

Join

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

3 x^{4} - 2 x^{4} + 7 x^{4}

1 \times (- 3)

1 \times (- 5)

- \frac{36 x ^{3}}{42 x ^{2}}

3 x^{2} + 42 x + 39

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