What is 4/(x^2-25)+(x+2)/(x^2-2x-15) ?

The solution to 4/(x^2-25)+(x+2)/(x^2-2x-15) is (x^2+11x+22)/((x+5)(x-5)(x+3))

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simplify 4/(x^2-25)+(x+2)/(x^2-2x-15)

simplify

\frac{4}{x ^{2} - 25} + \frac{x + 2}{x ^{2} - 2 x - 15}

\frac{x ^{2} + 11 x + 22}{( x + 5 ) ( x - 5 ) ( x + 3 )}

Solution steps

\frac{4}{x ^{2} - 25} + \frac{x + 2}{x ^{2} - 2 x - 15}

Least Common Multiplier of

x^{2} - 25, x^{2} - 2 x - 15 : (x + 5) (x - 5) (x + 3)

Adjust Fractions based on the LCM

= \frac{4 ( x + 3 )}{( x + 5 ) ( x - 5 ) ( x + 3 )} + \frac{( x + 2 ) ( x + 5 )}{( x + 5 ) ( x - 5 ) ( x + 3 )}

Apply the fraction rule:

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

= \frac{4 ( x + 3 ) + ( x + 2 ) ( x + 5 )}{( x + 5 ) ( x - 5 ) ( x + 3 )}

Simplify

4 (x + 3) + (x + 2) (x + 5) : x^{2} + 11 x + 22

= \frac{x ^{2} + 11 x + 22}{( x + 5 ) ( x - 5 ) ( x + 3 )}

\frac{1}{2} x + 1

\frac{1}{2} x + 2

lo g_{\frac{2}{3}} (\frac{81}{16})

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

\frac{1}{\frac{- 3}{2}}

What is 4/(x^2-25)+(x+2)/(x^2-2x-15) ?
The solution to 4/(x^2-25)+(x+2)/(x^2-2x-15) is (x^2+11x+22)/((x+5)(x-5)(x+3))