What is 2/x+3/(x-1)-4/(x^2-x) ?

The solution to 2/x+3/(x-1)-4/(x^2-x) is (5x-6)/(x(x-1))

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simplify 2/x+3/(x-1)-4/(x^2-x)

simplify

\frac{2}{x} + \frac{3}{x - 1} - \frac{4}{x ^{2} - x}

\frac{5 x - 6}{x ( x - 1 )}

Solution steps

\frac{2}{x} + \frac{3}{x - 1} - \frac{4}{x ^{2} - x}

Least Common Multiplier of

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

Adjust Fractions based on the LCM

= \frac{2 ( x - 1 )}{x ( x - 1 )} + \frac{3 x}{x ( x - 1 )} - \frac{4}{x ( x - 1 )}

Apply the fraction rule:

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

= \frac{2 ( x - 1 ) + 3 x - 4}{x ( x - 1 )}

Simplify

2 (x - 1) + 3 x - 4 : 5 x - 6

= \frac{5 x - 6}{x ( x - 1 )}

(x - 1) (2 x + 3)

6 x^{2} - 9 x

2 x + 3 x^{2}

\frac{x ^{2} - 5 x + 6}{2 a x - 6 a}

\frac{4 2}{2}

What is 2/x+3/(x-1)-4/(x^2-x) ?
The solution to 2/x+3/(x-1)-4/(x^2-x) is (5x-6)/(x(x-1))