What is x/(x^2+7x+12)+4/(x^2-16) ?

The solution to x/(x^2+7x+12)+4/(x^2-16) is (x^2+12)/((x+3)(x+4)(x-4))

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simplify x/(x^2+7x+12)+4/(x^2-16)

simplify

\frac{x}{x ^{2} + 7 x + 12} + \frac{4}{x ^{2} - 16}

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

Solution steps

\frac{x}{x ^{2} + 7 x + 12} + \frac{4}{x ^{2} - 16}

Least Common Multiplier of

x^{2} + 7 x + 12, x^{2} - 16 : (x + 3) (x + 4) (x - 4)

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

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

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

\frac{2 x ^{2}}{x ^{3} + x ^{2}}

(x + 1) (x + 1)

2100

\frac{45}{15}

(a + 2) (a - 2)

What is x/(x^2+7x+12)+4/(x^2-16) ?
The solution to x/(x^2+7x+12)+4/(x^2-16) is (x^2+12)/((x+3)(x+4)(x-4))