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

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

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

simplify

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

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

Solution steps

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

Least Common Multiplier of

x (x - 1), (x - 1) (x - 2) : x (x - 1) (x - 2)

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Cancel

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

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

50 \cdot 8

(\frac{1 - i}{3 + 3 i})^{4}

\frac{81}{18}

\frac{12 t ^{5}}{( 4 t ^{2} ) ^{4}}

\frac{y}{4 y + 8} - \frac{1}{y ^{2} + 2 y}

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