What is 3/(x^2+8x+16)+8/(x^2+x-12) ?

The solution to 3/(x^2+8x+16)+8/(x^2+x-12) is (11x+23)/((x+4)^2(x-3))

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simplify 3/(x^2+8x+16)+8/(x^2+x-12)

simplify

\frac{3}{x ^{2} + 8 x + 16} + \frac{8}{x ^{2} + x - 12}

\frac{11 x + 23}{( x + 4 ) ^{2} ( x - 3 )}

Solution steps

\frac{3}{x ^{2} + 8 x + 16} + \frac{8}{x ^{2} + x - 12}

Least Common Multiplier of

x^{2} + 8 x + 16, x^{2} + x - 12 : (x + 4)^{2} (x - 3)

Adjust Fractions based on the LCM

= \frac{3 ( x - 3 )}{( x + 4 ) ^{2} ( x - 3 )} + \frac{8 ( x + 4 )}{( x + 4 ) ^{2} ( x - 3 )}

Apply the fraction rule:

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

= \frac{3 ( x - 3 ) + 8 ( x + 4 )}{( x + 4 ) ^{2} ( x - 3 )}

Simplify

3 (x - 3) + 8 (x + 4) : 11 x + 23

= \frac{11 x + 23}{( x + 4 ) ^{2} ( x - 3 )}

\frac{125}{4}

(5 a - 2 b) (5 a + 2 b)

(4 v)^{2}

x^{5} y^{3} (- 2 x^{3} y)

512 x^{2}

What is 3/(x^2+8x+16)+8/(x^2+x-12) ?
The solution to 3/(x^2+8x+16)+8/(x^2+x-12) is (11x+23)/((x+4)^2(x-3))