What is (x^2+x-6)/(x^2+9x+14)-8/(x+7) ?

The solution to (x^2+x-6)/(x^2+9x+14)-8/(x+7) is (x^2-7x-22)/((x+2)(x+7))

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simplify (x^2+x-6)/(x^2+9x+14)-8/(x+7)

simplify

\frac{x ^{2} + x - 6}{x ^{2} + 9 x + 14} - \frac{8}{x + 7}

\frac{x ^{2} - 7 x - 22}{( x + 2 ) ( x + 7 )}

Solution steps

\frac{x ^{2} + x - 6}{x ^{2} + 9 x + 14} - \frac{8}{x + 7}

Least Common Multiplier of

x^{2} + 9 x + 14, x + 7 : (x + 2) (x + 7)

Adjust Fractions based on the LCM

= \frac{x ^{2} + x - 6}{( x + 2 ) ( x + 7 )} - \frac{8 ( x + 2 )}{( x + 2 ) ( x + 7 )}

Apply the fraction rule:

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

= \frac{x ^{2} + x - 6 - 8 ( x + 2 )}{( x + 2 ) ( x + 7 )}

Simplify

x^{2} + x - 6 - 8 (x + 2) : x^{2} - 7 x - 22

= \frac{x ^{2} - 7 x - 22}{( x + 2 ) ( x + 7 )}

cos (2 x) + cos (2 x)

\frac{4}{7} - \frac{1}{2}

\frac{1}{5} + \frac{3}{7}

\frac{2 x - 2}{2}

\frac{19}{16}

What is (x^2+x-6)/(x^2+9x+14)-8/(x+7) ?
The solution to (x^2+x-6)/(x^2+9x+14)-8/(x+7) is (x^2-7x-22)/((x+2)(x+7))