Question

How do you combine like terms in `\frac { 3k } { 5k - 30} - \frac { 6} { k + 1}`?

Answer 1

What you are actually doing is expressing the difference between two rational functions as a single rational function.

We can say:

`(3k)/(5k - 30) - 6/(k + 1) => (3k)/(5(k - 6)) - 6/(k + 1)`

Hence, a common denominator is 5(k - 6)(k + 1)

i.e. `[3k(k + 1) - 30(k - 6)]/(5(k - 6)(k + 1))`

so, `[3k^2 + 3k - 30k + 180]/(5(k - 6)(k + 1))`

=> `(3k^2 - 27k + 180)/(5(k - 6)(k + 1))`