What is expand 5/x-3/((x^2+2x+8)) ?

The solution to expand 5/x-3/((x^2+2x+8)) is (5x^2+7x+40)/(x^3+2x^2+8x)

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expand 5/x-3/((x^2+2x+8))

expand

\frac{5}{x} - \frac{3}{( x ^{2} + 2 x + 8 )}

\frac{5 x ^{2} + 7 x + 40}{x ^{3} + 2 x ^{2} + 8 x}

Solution steps

\frac{5}{x} - \frac{3}{x ^{2} + 2 x + 8}

Least Common Multiplier of

x, x^{2} + 2 x + 8 : x (x^{2} + 2 x + 8)

Adjust Fractions based on the LCM

= \frac{5 ( x ^{2} + 2 x + 8 )}{x ( x ^{2} + 2 x + 8 )} - \frac{3 x}{( x ^{2} + 2 x + 8 ) x}

Since the denominators are equal, combine the fractions:

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

= \frac{5 ( x ^{2} + 2 x + 8 ) - 3 x}{x ( x ^{2} + 2 x + 8 )}

Expand

x (x^{2} + 2 x + 8) : x^{3} + 2 x^{2} + 8 x

= \frac{5 ( x ^{2} + 2 x + 8 ) - 3 x}{x ^{3} + 2 x ^{2} + 8 x}

Expand

5 (x^{2} + 2 x + 8) - 3 x : 5 x^{2} + 7 x + 40

= \frac{5 x ^{2} + 7 x + 40}{x ^{3} + 2 x ^{2} + 8 x}

(1 + sin (2 x))^{2}

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

\frac{( y ^{3} ( 250 x y - 75 ) )}{( 5 x y - 1 ) ^{3}}

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

e^{1 + t} u (- t + 2)

What is expand 5/x-3/((x^2+2x+8)) ?
The solution to expand 5/x-3/((x^2+2x+8)) is (5x^2+7x+40)/(x^3+2x^2+8x)