What is (5x)/(x+8)+(4x-9)/(x^2+5x-24) ?

The solution to (5x)/(x+8)+(4x-9)/(x^2+5x-24) is (5x^2-11x-9)/((x+8)(x-3))

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simplify (5x)/(x+8)+(4x-9)/(x^2+5x-24)

simplify

\frac{5 x}{x + 8} + \frac{4 x - 9}{x ^{2} + 5 x - 24}

\frac{5 x ^{2} - 11 x - 9}{( x + 8 ) ( x - 3 )}

Solution steps

\frac{5 x}{x + 8} + \frac{4 x - 9}{x ^{2} + 5 x - 24}

Least Common Multiplier of

x + 8, x^{2} + 5 x - 24 : (x + 8) (x - 3)

Adjust Fractions based on the LCM

= \frac{5 x ( x - 3 )}{( x + 8 ) ( x - 3 )} + \frac{4 x - 9}{( x + 8 ) ( x - 3 )}

Apply the fraction rule:

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

= \frac{5 x ( x - 3 ) + 4 x - 9}{( x + 8 ) ( x - 3 )}

Simplify

5 x (x - 3) + 4 x - 9 : 5 x^{2} - 11 x - 9

= \frac{5 x ^{2} - 11 x - 9}{( x + 8 ) ( x - 3 )}

x^{3} \cdot x^{- 2}

(s^{2} + 2 s + 2)^{2}

\frac{e ^{t} ( 2 e ^{t} ) ^{2}}{e ^{- t}}

5 p + 3 p + (- 9)

\frac{p ^{6}}{p ^{- 2}}

What is (5x)/(x+8)+(4x-9)/(x^2+5x-24) ?
The solution to (5x)/(x+8)+(4x-9)/(x^2+5x-24) is (5x^2-11x-9)/((x+8)(x-3))