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

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

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

simplify

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

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

Solution steps

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

Least Common Multiplier of

x - 1, x : x (x - 1)

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

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

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

4 x - [6 x + (x - 4)]

\frac{x ^{2} - 4 x - 32}{x ^{2} - 16}

(4 + 5 m)^{3}

\frac{11}{6} \cdot \frac{5}{7}

(r^{2} - 8 r - 2) (- r^{2} + 3 r - 1)