Question

How do you divide `\frac { \frac { 5} { c b ^ { 2} } - \frac { 7} { c ^ { 2} d } } { \frac { 2} { c ^ { 2} d ^ { 2} } + \frac { 9} { c d } }`?

Answer 1

`=(d(5cd-7b^2))/(b^2(2+9cd))`

Explanation:

This can be written as a division of 2 algebraic fractions:

`color(red)((5/(cb^2) -7/(c^2d))) div color(blue)((2/(c^2d^2)+9/(cd)))`

Find the LCM for each fraction first and find equivalent fractions.
(the process is shown at the bottom)

`=color(red)((5cd-7b^2)/(b^2c^2d)) div color(blue)((2+9cd)/(c^2d^2))`

Multiply by the reciprocal of the second fraction:

`= color(red)(((5cd-7b^2))/(b^2cancel(c^2)d)) xx color(blue)((cancel(c^2)d^2)/((2+9cd))`

`=(d(5cd-7b^2))/(b^2(2+9cd))`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(red)(5/(cb^2) xx (cd)/(cd) = (5cd) /(b^2c^2d)`

`color(red)(7/(c^2d) xx b^2/b^2 = (7b^2)/(b^2c^2d))`

`color(blue)(9/(cd) xx (cd)/(cd) = (9cd)/(c^2d^2)`