What is (2x+7)/(x-6)-x/(x^2-3x-18) ?

The solution to (2x+7)/(x-6)-x/(x^2-3x-18) is (2x^2+12x+21)/((x-6)(x+3))

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simplify (2x+7)/(x-6)-x/(x^2-3x-18)

simplify

\frac{2 x + 7}{x - 6} - \frac{x}{x ^{2} - 3 x - 18}

\frac{2 x ^{2} + 12 x + 21}{( x - 6 ) ( x + 3 )}

Solution steps

\frac{2 x + 7}{x - 6} - \frac{x}{x ^{2} - 3 x - 18}

Least Common Multiplier of

x - 6, x^{2} - 3 x - 18 : (x - 6) (x + 3)

Adjust Fractions based on the LCM

= \frac{( 2 x + 7 ) ( x + 3 )}{( x - 6 ) ( x + 3 )} - \frac{x}{( x - 6 ) ( x + 3 )}

Apply the fraction rule:

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

= \frac{( 2 x + 7 ) ( x + 3 ) - x}{( x - 6 ) ( x + 3 )}

Simplify

(2 x + 7) (x + 3) - x : 2 x^{2} + 12 x + 21

= \frac{2 x ^{2} + 12 x + 21}{( x - 6 ) ( x + 3 )}

\frac{3}{60}

\frac{8 x}{2 x}

3 (x - 3)

(x + 10) (x^{2} - 2 x + 3)

\frac{2}{x} + 1

What is (2x+7)/(x-6)-x/(x^2-3x-18) ?
The solution to (2x+7)/(x-6)-x/(x^2-3x-18) is (2x^2+12x+21)/((x-6)(x+3))