What is expand (x(3x+4))/(2(x+1)^{3/2)} ?

The solution to expand (x(3x+4))/(2(x+1)^{3/2)} is (3x^2)/(2(x+1)^{3/2)}+(2x)/((x+1)^{3/2)}

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expand (x(3x+4))/(2(x+1)^{3/2)}

expand

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

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

Solution steps

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

Expand

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

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

Apply the fraction rule:

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

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

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

Divide the numbers:

\frac{4}{2} = 2

= \frac{3 x ^{2}}{2 ( x + 1 ) ^{\frac{3}{2}}} + \frac{2 x}{( x + 1 ) ^{\frac{3}{2}}}

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

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What is expand (x(3x+4))/(2(x+1)^{3/2)} ?
The solution to expand (x(3x+4))/(2(x+1)^{3/2)} is (3x^2)/(2(x+1)^{3/2)}+(2x)/((x+1)^{3/2)}