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Popular >

expand ((x^2+1)^2)/x

Solution

expand

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

Solution

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

Solution steps

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

(x^{2} + 1)^{2} = x^{4} + 2 x^{2} + 1

= \frac{x ^{4} + 2 x ^{2} + 1}{x}

Apply the fraction rule:

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

\frac{x ^{4} + 2 x ^{2} + 1}{x} = \frac{x ^{4}}{x} + \frac{2 x ^{2}}{x} + \frac{1}{x}

= \frac{x ^{4}}{x} + \frac{2 x ^{2}}{x} + \frac{1}{x}

Cancel

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

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

Cancel

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

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

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Frequently Asked Questions (FAQ)

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