What is x/(x-3)+(5x+1)/(x+8) ?

The solution to x/(x-3)+(5x+1)/(x+8) is (6x^2-6x-3)/((x-3)(x+8))

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simplify x/(x-3)+(5x+1)/(x+8)

simplify

\frac{x}{x - 3} + \frac{5 x + 1}{x + 8}

\frac{6 x ^{2} - 6 x - 3}{( x - 3 ) ( x + 8 )}

Solution steps

\frac{x}{x - 3} + \frac{5 x + 1}{x + 8}

Least Common Multiplier of

x - 3, x + 8 : (x - 3) (x + 8)

Adjust Fractions based on the LCM

= \frac{x ( x + 8 )}{( x - 3 ) ( x + 8 )} + \frac{( 5 x + 1 ) ( x - 3 )}{( x - 3 ) ( x + 8 )}

Apply the fraction rule:

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

= \frac{x ( x + 8 ) + ( 5 x + 1 ) ( x - 3 )}{( x - 3 ) ( x + 8 )}

Simplify

x (x + 8) + (5 x + 1) (x - 3) : 6 x^{2} - 6 x - 3

= \frac{6 x ^{2} - 6 x - 3}{( x - 3 ) ( x + 8 )}

(x^{2} - 2) (x^{2} + 3 x + 5)

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

\frac{36}{48}

- 2 - \frac{12}{3}

(2 x - 3)^{5}

What is x/(x-3)+(5x+1)/(x+8) ?
The solution to x/(x-3)+(5x+1)/(x+8) is (6x^2-6x-3)/((x-3)(x+8))