Multiplication & Division with Algebraic Fractions (SQA National 5 Maths): Revision Note

Express $\frac{5}{x+3}÷\frac{6}{{\left(x+3\right)}^2},x\ne -3,$ as a single fraction in its simplest form.

Answer:

Division is the same as multiplying by the reciprocal (the fraction flipped)

$\frac{5}{x+3}÷\frac{6}{{\left(x+3\right)}^2}=\frac{5}{x+3}\times \frac{{\left(x+3\right)}^2}{6}$

Check the numerators and denominators to see if any factors cancel out

• Remember that ${\left(x+3\right)}^2=\left(x+3\right)\left(x+3\right)$

$$\begin{gathered} =\frac{5}{1\cancel{x+3}}\times \frac{\left(x+3\right)\cancel{\left(x+3\right)}}{6} \\ =\frac{5}{1}\times \frac{x+3}{6} \end{gathered}$$

Multiply the remaining numerators and denominators together

$=\frac{5\left(x+3\right)}{6}$

There are no other factors that can be cancelled, so that answer is in simplest form

$\frac{5\left(x+3\right)}{6}\left(\mathrm{or}\frac{5x+15}{6}\mathrm{or}\frac{5}{6}\left(x+3\right)\right)$

For the purpose of multiplying and dividing algebraic fractions in questions like the Worked Example, you can disregard conditions like "$x\ne -3$".

That is just there to make sure that the denominators of the fractions can never be equal to zero.