What is expand ((x+2)^2)/(x^2) ?

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

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

expand

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

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

Solution steps

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

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

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

Apply the fraction rule:

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

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

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

Apply rule

\frac{a}{a} = 1

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

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

Cancel

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

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

\frac{1}{( ( a ) + 4 ) ^{2}}

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