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

The solution to 3/(x-3)-5/(x+2) is (-2x+21)/((x-3)(x+2))

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

simplify

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

\frac{- 2 x + 21}{( x - 3 ) ( x + 2 )}

Solution steps

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

Least Common Multiplier of

x - 3, x + 2 : (x - 3) (x + 2)

Adjust Fractions based on the LCM

= \frac{3 ( x + 2 )}{( x - 3 ) ( x + 2 )} - \frac{5 ( x - 3 )}{( x - 3 ) ( x + 2 )}

Apply the fraction rule:

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

= \frac{3 ( x + 2 ) - 5 ( x - 3 )}{( x - 3 ) ( x + 2 )}

Simplify

3 (x + 2) - 5 (x - 3) : - 2 x + 21

= \frac{- 2 x + 21}{( x - 3 ) ( x + 2 )}

\frac{73}{4}

h (6)

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

(5 a)^{\frac{3}{5}}

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

What is 3/(x-3)-5/(x+2) ?
The solution to 3/(x-3)-5/(x+2) is (-2x+21)/((x-3)(x+2))