What is x/(x-4)-3/(x+6) ?

The solution to x/(x-4)-3/(x+6) is (x^2+3x+12)/((x-4)(x+6))

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simplify x/(x-4)-3/(x+6)

simplify

\frac{x}{x - 4} - \frac{3}{x + 6}

\frac{x ^{2} + 3 x + 12}{( x - 4 ) ( x + 6 )}

Solution steps

\frac{x}{x - 4} - \frac{3}{x + 6}

Least Common Multiplier of

x - 4, x + 6 : (x - 4) (x + 6)

Adjust Fractions based on the LCM

= \frac{x ( x + 6 )}{( x - 4 ) ( x + 6 )} - \frac{3 ( x - 4 )}{( x - 4 ) ( x + 6 )}

Apply the fraction rule:

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

= \frac{x ( x + 6 ) - 3 ( x - 4 )}{( x - 4 ) ( x + 6 )}

Simplify

x (x + 6) - 3 (x - 4) : x^{2} + 3 x + 12

= \frac{x ^{2} + 3 x + 12}{( x - 4 ) ( x + 6 )}

(x - 5) (x + 9)

- 18 \div 2

\frac{1}{\frac{x}{x + 1}}

7 z^{2} - 38 z + 15

6 x + 20

What is x/(x-4)-3/(x+6) ?
The solution to x/(x-4)-3/(x+6) is (x^2+3x+12)/((x-4)(x+6))