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

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

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

simplify

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

\frac{x ^{2} + 4 x - 6}{x ( x - 2 )}

Solution steps

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

Least Common Multiplier of

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

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

3 x + (x + 3) (x - 2) : x^{2} + 4 x - 6

= \frac{x ^{2} + 4 x - 6}{x ( x - 2 )}

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

\frac{- 4 x - 32}{x ^{2} - 12 x + 36} \cdot \frac{x ^{2} - 9 x + 18}{3 x + 24}

(x - 8) (x - 11)

x + 2 x + 3 x

\frac{\frac{4}{3}}{\frac{2}{3}}

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