What is 3/x+5/(x-1) ?

The solution to 3/x+5/(x-1) is (8x-3)/(x(x-1))

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simplify 3/x+5/(x-1)

simplify

\frac{3}{x} + \frac{5}{x - 1}

\frac{8 x - 3}{x ( x - 1 )}

Solution steps

\frac{3}{x} + \frac{5}{x - 1}

Least Common Multiplier of

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

Adjust Fractions based on the LCM

= \frac{3 ( x - 1 )}{x ( x - 1 )} + \frac{5 x}{x ( x - 1 )}

Apply the fraction rule:

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

= \frac{3 ( x - 1 ) + 5 x}{x ( x - 1 )}

Simplify

3 (x - 1) + 5 x : 8 x - 3

= \frac{8 x - 3}{x ( x - 1 )}

6 \cdot 14

4 x^{3} - 2 x

3 (2 x^{2} - 1)

(x^{4} - 1)^{2}

\frac{3 b - 5}{b ^{2}} \cdot \frac{b ^{4}}{5 - 3 b}