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

The solution to expand 4/(x^2-25)+(x+2)/(x^2-2x-15) is (x^2+11x+22)/(x^3+3x^2-25x-75)

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

expand

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

\frac{x ^{2} + 11 x + 22}{x ^{3} + 3 x ^{2} - 25 x - 75}

Solution steps

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

Factor

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

= \frac{4}{( x + 5 ) ( x - 5 )} + \frac{x + 2}{x ^{2} - 2 x - 15}

Factor

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

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

Least Common Multiplier of

(x + 5) (x - 5), (x + 3) (x - 5) : (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 + 3 ) ( x - 5 ) ( x + 5 )}

Since the denominators are equal, combine the fractions:

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

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

Expand

(x + 5) (x - 5) (x + 3) : x^{3} + 3 x^{2} - 25 x - 75

= \frac{4 ( x + 3 ) + ( x + 2 ) ( x + 5 )}{x ^{3} + 3 x ^{2} - 25 x - 75}

Expand

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

= \frac{x ^{2} + 11 x + 22}{x ^{3} + 3 x ^{2} - 25 x - 75}

, (t - \frac{1}{2}) sin (2 π t)

(3 x - 2) (2 x + 5)

B (x + 1) (x + i) (x - i)^{2} + D (x + 1) (x - i) (x + i)^{2}

(A + B x) e^{3 x}

\frac{( 3 x + 1 ) ^{4} ( x - 4 )}{( x ^{2} + 1 ) ^{3} sin ( x )}

What is expand 4/(x^2-25)+(x+2)/(x^2-2x-15) ?
The solution to expand 4/(x^2-25)+(x+2)/(x^2-2x-15) is (x^2+11x+22)/(x^3+3x^2-25x-75)