What is 7/(x+6)-(6x)/(x^2-36) ?

The solution to 7/(x+6)-(6x)/(x^2-36) is (x-42)/((x+6)(x-6))

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simplify 7/(x+6)-(6x)/(x^2-36)

simplify

\frac{7}{x + 6} - \frac{6 x}{x ^{2} - 36}

\frac{x - 42}{( x + 6 ) ( x - 6 )}

Solution steps

\frac{7}{x + 6} - \frac{6 x}{x ^{2} - 36}

Least Common Multiplier of

x + 6, x^{2} - 36 : (x + 6) (x - 6)

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

7 (x - 6) - 6 x : x - 42

= \frac{x - 42}{( x + 6 ) ( x - 6 )}

8 \times 8 \times 8 \times 8 \times 8 \times 8

(\frac{4}{2 ^{2}})^{2 + 2}

\frac{172000}{9}

\frac{6 - - 8}{2}

x^{3} - 31 x - 30

What is 7/(x+6)-(6x)/(x^2-36) ?
The solution to 7/(x+6)-(6x)/(x^2-36) is (x-42)/((x+6)(x-6))