What is 5/(x^2-x-42)-(5x)/(x+6) ?

The solution to 5/(x^2-x-42)-(5x)/(x+6) is (5-5x^2+35x)/((x+6)(x-7))

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simplify 5/(x^2-x-42)-(5x)/(x+6)

simplify

\frac{5}{x ^{2} - x - 42} - \frac{5 x}{x + 6}

\frac{5 - 5 x ^{2} + 35 x}{( x + 6 ) ( x - 7 )}

Solution steps

\frac{5}{x ^{2} - x - 42} - \frac{5 x}{x + 6}

Least Common Multiplier of

x^{2} - x - 42, x + 6 : (x + 6) (x - 7)

Adjust Fractions based on the LCM

= \frac{5}{( x + 6 ) ( x - 7 )} - \frac{5 x ( x - 7 )}{( x + 6 ) ( x - 7 )}

Apply the fraction rule:

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

= \frac{5 - 5 x ( x - 7 )}{( x + 6 ) ( x - 7 )}

Simplify

5 - 5 x (x - 7) : 5 - 5 x^{2} + 35 x

= \frac{5 - 5 x ^{2} + 35 x}{( x + 6 ) ( x - 7 )}

\frac{n}{n}

(a + b)^{3} - (a + b) (a^{2} + b^{2}) - 2 a b^{2}

5 + (- 1)

(y + 3) (y - 5)

- 3 x^{2} y + 15 x^{2} y - 24 x^{2} y

What is 5/(x^2-x-42)-(5x)/(x+6) ?
The solution to 5/(x^2-x-42)-(5x)/(x+6) is (5-5x^2+35x)/((x+6)(x-7))