What is expand (a-c-b(q(n-1)))/(2b) ?

The solution to expand (a-c-b(q(n-1)))/(2b) is a/(2b)-c/(2b)-(nq)/2+q/2

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expand (a-c-b(q(n-1)))/(2b)

expand

\frac{a - c - b ( q ( n - 1 ) )}{2 b}

\frac{a}{2 b} - \frac{c}{2 b} - \frac{n q}{2} + \frac{q}{2}

Solution steps

\frac{a - c - b ( q ( n - 1 ) )}{2 b}

Remove parentheses:

(a) = a

= \frac{a - c - b q ( n - 1 )}{2 b}

Expand

a - c - b q (n - 1) : a - c - bn q + b q

= \frac{a - c - bn q + b q}{2 b}

Apply the fraction rule:

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

\frac{a - c - bn q + b q}{2 b} = \frac{a}{2 b} - \frac{c}{2 b} - \frac{bn q}{2 b} + \frac{b q}{2 b}

= \frac{a}{2 b} - \frac{c}{2 b} - \frac{bn q}{2 b} + \frac{b q}{2 b}

Cancel

\frac{bn q}{2 b} : \frac{n q}{2}

= \frac{a}{2 b} - \frac{c}{2 b} - \frac{n q}{2} + \frac{b q}{2 b}

Cancel

\frac{b q}{2 b} : \frac{q}{2}

= \frac{a}{2 b} - \frac{c}{2 b} - \frac{n q}{2} + \frac{q}{2}

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What is expand (a-c-b(q(n-1)))/(2b) ?
The solution to expand (a-c-b(q(n-1)))/(2b) is a/(2b)-c/(2b)-(nq)/2+q/2