What is (5x)/(x^2+4x-12)-4/(x-2) ?

The solution to (5x)/(x^2+4x-12)-4/(x-2) is (x-24)/((x-2)(x+6))

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simplify (5x)/(x^2+4x-12)-4/(x-2)

simplify

\frac{5 x}{x ^{2} + 4 x - 12} - \frac{4}{x - 2}

\frac{x - 24}{( x - 2 ) ( x + 6 )}

Solution steps

\frac{5 x}{x ^{2} + 4 x - 12} - \frac{4}{x - 2}

Least Common Multiplier of

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

Adjust Fractions based on the LCM

= \frac{5 x}{( x - 2 ) ( x + 6 )} - \frac{4 ( x + 6 )}{( x - 2 ) ( x + 6 )}

Apply the fraction rule:

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

= \frac{5 x - 4 ( x + 6 )}{( x - 2 ) ( x + 6 )}

Simplify

5 x - 4 (x + 6) : x - 24

= \frac{x - 24}{( x - 2 ) ( x + 6 )}

\frac{( - x ^{3} ) ^{2}}{( - x ) ^{- 3}}

(1 + \frac{1}{5})^{5}

1 + tan^{2} (a)

(2 m - 5) (2 m - 3) - (m^{2} + 5 m)

2 x^{3} + 2 x^{3}

What is (5x)/(x^2+4x-12)-4/(x-2) ?
The solution to (5x)/(x^2+4x-12)-4/(x-2) is (x-24)/((x-2)(x+6))