What is x/(x^2+2x-8)+(x+3)/(x^2-3x+2) ?

The solution to x/(x^2+2x-8)+(x+3)/(x^2-3x+2) is (2x^2+6x+12)/((x-2)(x+4)(x-1))

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simplify x/(x^2+2x-8)+(x+3)/(x^2-3x+2)

simplify

\frac{x}{x ^{2} + 2 x - 8} + \frac{x + 3}{x ^{2} - 3 x + 2}

\frac{2 x ^{2} + 6 x + 12}{( x - 2 ) ( x + 4 ) ( x - 1 )}

Solution steps

\frac{x}{x ^{2} + 2 x - 8} + \frac{x + 3}{x ^{2} - 3 x + 2}

Least Common Multiplier of

x^{2} + 2 x - 8, x^{2} - 3 x + 2 : (x - 2) (x + 4) (x - 1)

Adjust Fractions based on the LCM

= \frac{x ( x - 1 )}{( x - 2 ) ( x + 4 ) ( x - 1 )} + \frac{( x + 3 ) ( x + 4 )}{( x - 2 ) ( x + 4 ) ( x - 1 )}

Apply the fraction rule:

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

= \frac{x ( x - 1 ) + ( x + 3 ) ( x + 4 )}{( x - 2 ) ( x + 4 ) ( x - 1 )}

Simplify

x (x - 1) + (x + 3) (x + 4) : 2 x^{2} + 6 x + 12

= \frac{2 x ^{2} + 6 x + 12}{( x - 2 ) ( x + 4 ) ( x - 1 )}

(2 x - 2) (x + 1)

\frac{1}{1 - ( \frac{x ^{2}}{1 - x ^{3}} + \frac{x ^{3}}{1 - x ^{2}} )}

\frac{5}{4} + \frac{3}{4} \cdot \frac{1}{6}

3 x^{3} - 2 x - 1

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

What is x/(x^2+2x-8)+(x+3)/(x^2-3x+2) ?
The solution to x/(x^2+2x-8)+(x+3)/(x^2-3x+2) is (2x^2+6x+12)/((x-2)(x+4)(x-1))