What is expand ((a-b)^2)/(2ab) ?

The solution to expand ((a-b)^2)/(2ab) is a/(2b)-1+b/(2a)

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expand ((a-b)^2)/(2ab)

expand

\frac{( a - b ) ^{2}}{2 ab}

\frac{a}{2 b} - 1 + \frac{b}{2 a}

Solution steps

\frac{( a - b ) ^{2}}{2 ab}

(a - b)^{2} = a^{2} - 2 ab + b^{2}

= \frac{a ^{2} - 2 ab + b ^{2}}{2 ab}

Apply the fraction rule:

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

\frac{a ^{2} - 2 ab + b ^{2}}{2 ab} = \frac{a ^{2}}{2 ab} - \frac{2 ab}{2 ab} + \frac{b ^{2}}{2 ab}

= \frac{a ^{2}}{2 ab} - \frac{2 ab}{2 ab} + \frac{b ^{2}}{2 ab}

Apply rule

\frac{a}{a} = 1

\frac{2 ab}{2 ab} = 1

= \frac{a ^{2}}{2 ab} - 1 + \frac{b ^{2}}{2 ab}

Cancel

\frac{a ^{2}}{2 ab} : \frac{a}{2 b}

= \frac{a}{2 b} - 1 + \frac{b ^{2}}{2 ab}

Cancel

\frac{b ^{2}}{2 ab} : \frac{b}{2 a}

= \frac{a}{2 b} - 1 + \frac{b}{2 a}

a (- 3, 5) b (7, 3) c (8, - 4)

(16 x + 5 y) d x + (3 x + y) d y

\frac{5 x ^{2} + 5 x - 4}{5 ( x - 4 )}

(y - x = 0,) (x + y = 1)

(3 e^{4} - 5 f)^{2}

What is expand ((a-b)^2)/(2ab) ?
The solution to expand ((a-b)^2)/(2ab) is a/(2b)-1+b/(2a)