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

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

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

expand

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

\frac{4}{3 x ^{2}} - \frac{4}{3 x ^{3}}

Solution steps

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

Divide fractions:

\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a \cdot d}{b \cdot c}

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

Cancel the common factor:

x

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

Factor

4 (x^{2} - 1) : 4 (x + 1) (x - 1)

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

Cancel the common factor:

x + 1

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

Expand

4 (x - 1) : 4 x - 4

= \frac{4 x - 4}{3 x ^{3}}

Apply the fraction rule:

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

\frac{4 x - 4}{3 x ^{3}} = \frac{4 x}{3 x ^{3}} - \frac{4}{3 x ^{3}}

= \frac{4 x}{3 x ^{3}} - \frac{4}{3 x ^{3}}

Cancel

\frac{4 x}{3 x ^{3}} : \frac{4}{3 x ^{2}}

= \frac{4}{3 x ^{2}} - \frac{4}{3 x ^{3}}

ln (x) (x + 9)

(1 - x - 3)^{2}

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

(\frac{6}{5 π , - 3.7}) (π, - 11)

\frac{x - cos ( x ) ( m x + 1 ) - arctan ( x ) + 1}{x ^{4} ( m + 1 )}

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