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

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

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

expand

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

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

Solution steps

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

Expand

(x + 1) (2 x + 1) : 2 x^{2} + 3 x + 1

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

Apply the fraction rule:

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

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

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

Cancel

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

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

Cancel

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

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

3 (x + h)^{2} - 1 - 3 x^{2} - 1

\frac{36 x}{( x ^{2} + 9 ) ^{2}}

cos (x) (1 - sin (x))

\frac{1 - 2 e ^{- s}}{s ^{2} ( s ^{2} + 1 )}

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

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