Dividing algebraic fractions

When dividing fractions, keep the first fraction as it is, change the divide sign to a multiply and flip the second fraction upside down.

One way to remember this is:

Keep it, change it, flip it

Calculate \(\frac{3}{8} \div \frac{3}{4}\)

\(= \frac{3}{8} \times \frac{4}{3}\)

Keep it, change it, flip it:

\(= \frac{{3 \times 4}}{{8 \times 3}}\)

Now use the same method as multiplying fractions:

\(= \frac{{1 \times 1}}{{2 \times 1}}\)

Remember to look out for common factors that can cancel – in this case divide both top and bottom by 3 and also 4.

\(= \frac{1}{2}\)

Question

Calculate \(\frac{9}{z} \div \frac{{(z + 1)}}{{(z - 8)}}\)