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

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

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

simplify

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

\frac{5 x - 2}{x ( x - 1 )}

Solution steps

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

Least Common Multiplier of

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

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

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

= \frac{5 x - 2}{x ( x - 1 )}

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

\frac{63}{27}

2 - 52

(1 0^{3} \cdot 1 0^{2}) + 1 0^{- 3}

\frac{63}{10}