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

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

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

simplify

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

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

Solution steps

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

Least Common Multiplier of

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

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

5 x + 1 - (x - 1) : 4 x + 2

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

\frac{3}{2} x^{\frac{1}{2}}

2 x^{3} + 3 x^{2} - 36 x

(6 - 54) (- 57)

- \frac{1}{2} + i \frac{3}{2}

\frac{4 ^{8}}{4 ^{- 4}}

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