What is 3/(2x)+5/(x-2) ?

The solution to 3/(2x)+5/(x-2) is (13x-6)/(2x(x-2))

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simplify 3/(2x)+5/(x-2)

simplify

\frac{3}{2 x} + \frac{5}{x - 2}

\frac{13 x - 6}{2 x ( x - 2 )}

Solution steps

\frac{3}{2 x} + \frac{5}{x - 2}

Least Common Multiplier of

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

Adjust Fractions based on the LCM

= \frac{3 ( x - 2 )}{2 x ( x - 2 )} + \frac{10 x}{2 x ( x - 2 )}

Apply the fraction rule:

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

= \frac{3 ( x - 2 ) + 10 x}{2 x ( x - 2 )}

Simplify

3 (x - 2) + 10 x : 13 x - 6

= \frac{13 x - 6}{2 x ( x - 2 )}

x^{2} - 26 x + 169

- 10 \cdot - 24

(- 3 - i)^{12}

\frac{12}{42}

x (x - 2) (x - 3)