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

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

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

expand

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

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

Solution steps

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

(u + x)^{2} = u^{2} + 2 ux + x^{2}

= \frac{2 ( u ^{2} + 2 ux + x ^{2} )}{x ^{2}}

Expand

2 (u^{2} + 2 ux + x^{2}) : 2 u^{2} + 4 ux + 2 x^{2}

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

Apply the fraction rule:

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

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

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

Cancel

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

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

Cancel

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

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

(2 x^{3} + 3 x y^{2}) d y

21 (\frac{4}{7})

\frac{1}{5 \cdot ( c + 1 )}

\frac{( n - 1 ) n}{2}

\frac{n + 3}{( n + 1 ) ( n + 2 )}

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