Question

$$\frac{(e-3)^{2}}{2e+f}\div\frac{3e-9}{10e+5f}$$

Answer

(5*(e-3))/3

Solution


Factor out the common term \(3\).
\[\frac{\frac{{(e-3)}^{2}}{2e+f}}{\frac{3(e-3)}{10e+5f}}\]
Factor out the common term \(5\).
\[\frac{\frac{{(e-3)}^{2}}{2e+f}}{\frac{3(e-3)}{5(2e+f)}}\]
Invert and multiply.
\[\frac{{(e-3)}^{2}}{2e+f}\times \frac{5(2e+f)}{3(e-3)}\]
Cancel \(2e+f\).
\[{(e-3)}^{2}\times \frac{5}{3(e-3)}\]
Use this rule: \(a \times \frac{b}{c}=\frac{ab}{c}\).
\[\frac{{(e-3)}^{2}\times 5}{3(e-3)}\]
Regroup terms.
\[\frac{5{(e-3)}^{2}}{3(e-3)}\]
Simplify.
\[\frac{5(e-3)}{3}\]

Decimal Form: -0.469530