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Popular >

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

Solution

expand

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

Solution

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

Solution steps

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

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

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

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

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

Apply the fraction rule:

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

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

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

Apply rule

\frac{a}{a} = 1

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

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

Cancel

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

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

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Frequently Asked Questions (FAQ)

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