What is (-2x-2)/(x^2+2x-8)-(x-1)/(2-x) ?

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

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simplify (-2x-2)/(x^2+2x-8)-(x-1)/(2-x)

simplify

\frac{- 2 x - 2}{x ^{2} + 2 x - 8} - \frac{x - 1}{2 - x}

\frac{x + 3}{x + 4}

Solution steps

\frac{- 2 x - 2}{x ^{2} + 2 x - 8} - \frac{x - 1}{2 - x}

Least Common Multiplier of

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

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Apply rule:

a - (- b) = a + b

(- 2 x - 2) (- x + 2) - (- (x - 1) (x + 4) (- x + 2)) = (- 2 x - 2) (- x + 2) + (x - 1) (x + 4) (- x + 2)

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

Simplify

(- 2 x - 2) (- x + 2) + (x - 1) (x + 4) (- x + 2) : - x^{3} + x^{2} + 8 x - 12

= \frac{- x ^{3} + x ^{2} + 8 x - 12}{( x - 2 ) ( x + 4 ) ( - x + 2 )}

Cancel

\frac{- x ^{3} + x ^{2} + 8 x - 12}{( x - 2 ) ( x + 4 ) ( - x + 2 )} : \frac{x + 3}{x + 4}

= \frac{x + 3}{x + 4}

2 x^{2} \times x

x + 5 x

3 (x - 5)^{2}

\frac{7}{5 - u} - \frac{2 + u}{5 - u}

- \frac{3}{2} + 6

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