What is (5x-1)/(x^2+2x-8)-6/(x+4) ?

The solution to (5x-1)/(x^2+2x-8)-6/(x+4) is (-x+11)/((x-2)(x+4))

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simplify (5x-1)/(x^2+2x-8)-6/(x+4)

simplify

\frac{5 x - 1}{x ^{2} + 2 x - 8} - \frac{6}{x + 4}

\frac{- x + 11}{( x - 2 ) ( x + 4 )}

Solution steps

\frac{5 x - 1}{x ^{2} + 2 x - 8} - \frac{6}{x + 4}

Least Common Multiplier of

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

Adjust Fractions based on the LCM

= \frac{5 x - 1}{( x - 2 ) ( x + 4 )} - \frac{6 ( x - 2 )}{( x - 2 ) ( x + 4 )}

Apply the fraction rule:

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

= \frac{5 x - 1 - 6 ( x - 2 )}{( x - 2 ) ( x + 4 )}

Simplify

5 x - 1 - 6 (x - 2) : - x + 11

= \frac{- x + 11}{( x - 2 ) ( x + 4 )}

3 \frac{1}{4} - 2 \frac{1}{5} + \frac{11}{20}

\frac{- 19.3}{- 151.505} - 10

\frac{4}{2}

664

\frac{8}{3} \cdot \frac{5}{7} \cdot \frac{7}{3} \cdot \frac{3}{5} \cdot \frac{1}{2}

What is (5x-1)/(x^2+2x-8)-6/(x+4) ?
The solution to (5x-1)/(x^2+2x-8)-6/(x+4) is (-x+11)/((x-2)(x+4))