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

The solution to 1/x-1/(x-1) is -1/(x(x-1))

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

simplify

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

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

Solution steps

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

Least Common Multiplier of

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

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

x - 1 - x : - 1

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

Apply the fraction rule:

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

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

18 \div 9

\frac{x ^{2} - 1}{x ^{2} + 3 x + 2}

(3 x) (3 x)

36 - 37 x - 48 x^{2}

2 x (x + 2)