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

The solution to (x+4)/(x^2-x-12)+(2x)/(x-4) is (2x^2+7x+4)/((x+3)(x-4))

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

simplify

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

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

Solution steps

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

Least Common Multiplier of

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

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

x + 4 + 2 x (x + 3) : 2 x^{2} + 7 x + 4

= \frac{2 x ^{2} + 7 x + 4}{( x + 3 ) ( x - 4 )}

\frac{x ^{2} + 2 x y + y ^{2}}{x + y}

4 \cdot (- \frac{3}{2})

\frac{49}{6}

- 2 w z (6 w^{2} - 4 w z + 3 z^{2})

60 \cdot 40 \cdot 30

What is (x+4)/(x^2-x-12)+(2x)/(x-4) ?
The solution to (x+4)/(x^2-x-12)+(2x)/(x-4) is (2x^2+7x+4)/((x+3)(x-4))