What is (12)/(x^2+x-6)+4/(x-2) ?

The solution to (12)/(x^2+x-6)+4/(x-2) is (4x+24)/((x-2)(x+3))

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simplify (12)/(x^2+x-6)+4/(x-2)

simplify

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

\frac{4 x + 24}{( x - 2 ) ( x + 3 )}

Solution steps

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

Least Common Multiplier of

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

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

12 + 4 (x + 3) : 4 x + 24

= \frac{4 x + 24}{( x - 2 ) ( x + 3 )}

(x - (2 - i)) (x - (2 + i))

\frac{2 x ^{3} + 10 x ^{2} + 16 x + 8}{4 x ^{3} + 8 x ^{2} - 4 x - 8}

(2 x - 5) (4 x^{3} - 7 x^{2} + 2 x - 3)

ln (\frac{1}{e ^{11}})

4 - 4 x^{2}

What is (12)/(x^2+x-6)+4/(x-2) ?
The solution to (12)/(x^2+x-6)+4/(x-2) is (4x+24)/((x-2)(x+3))