What is expand (q(d-x)^2)/(x^2) ?

The solution to expand (q(d-x)^2)/(x^2) is (d^2q}{x^2}-\frac{2dq)/x+q

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expand (q(d-x)^2)/(x^2)

expand

\frac{q ( d - x ) ^{2}}{x ^{2}}

\frac{d ^{2} q}{x ^{2}} - \frac{2 d q}{x} + q

Solution steps

\frac{q ( d - x ) ^{2}}{x ^{2}}

(d - x)^{2} = d^{2} - 2 d x + x^{2}

= \frac{q ( x ^{2} - 2 d x + d ^{2} )}{x ^{2}}

Expand

q (d^{2} - 2 d x + x^{2}) : d^{2} q - 2 d q x + q x^{2}

= \frac{d ^{2} q - 2 d q x + q x ^{2}}{x ^{2}}

Apply the fraction rule:

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

\frac{d ^{2} q - 2 d q x + q x ^{2}}{x ^{2}} = \frac{d ^{2} q}{x ^{2}} - \frac{2 d q x}{x ^{2}} + \frac{q x ^{2}}{x ^{2}}

= \frac{d ^{2} q}{x ^{2}} - \frac{2 d q x}{x ^{2}} + \frac{q x ^{2}}{x ^{2}}

Cancel

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

= \frac{d ^{2} q}{x ^{2}} - \frac{2 d q}{x} + \frac{q x ^{2}}{x ^{2}}

Cancel

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

= \frac{d ^{2} q}{x ^{2}} - \frac{2 d q}{x} + q

\frac{1}{3 t ( 3 t - 2 ) ( 3 t + 2 )}

- \frac{4 x ^{2} - 41 x + 104}{( x - 4 ) ^{3}}

- (4 i - 4) \pm (4 i - 4)^{2} - 4 (1 - i) (3 - 11 i)

(\frac{x - 4}{2} + \frac{y}{1} - 2 = 0) 2

\frac{x ^{2} + 81}{x ( x ^{2} + 9 ) ^{2}}

What is expand (q(d-x)^2)/(x^2) ?
The solution to expand (q(d-x)^2)/(x^2) is (d^2q}{x^2}-\frac{2dq)/x+q