What is 3/(x-5)+(7x)/(x+8) ?

The solution to 3/(x-5)+(7x)/(x+8) is (7x^2-32x+24)/((x-5)(x+8))

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simplify 3/(x-5)+(7x)/(x+8)

simplify

\frac{3}{x - 5} + \frac{7 x}{x + 8}

\frac{7 x ^{2} - 32 x + 24}{( x - 5 ) ( x + 8 )}

Solution steps

\frac{3}{x - 5} + \frac{7 x}{x + 8}

Least Common Multiplier of

x - 5, x + 8 : (x - 5) (x + 8)

Adjust Fractions based on the LCM

= \frac{3 ( x + 8 )}{( x - 5 ) ( x + 8 )} + \frac{7 x ( x - 5 )}{( x - 5 ) ( x + 8 )}

Apply the fraction rule:

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

= \frac{3 ( x + 8 ) + 7 x ( x - 5 )}{( x - 5 ) ( x + 8 )}

Simplify

3 (x + 8) + 7 x (x - 5) : 7 x^{2} - 32 x + 24

= \frac{7 x ^{2} - 32 x + 24}{( x - 5 ) ( x + 8 )}

(3 x + 2) (2 x + 4)

1 \times (- 2)

\frac{1}{4} \times 3

(x + 1) (x^{2} - 5 x + 6)

\frac{3}{4} \times 2

What is 3/(x-5)+(7x)/(x+8) ?
The solution to 3/(x-5)+(7x)/(x+8) is (7x^2-32x+24)/((x-5)(x+8))