Question

How do you subtract `\frac { 2} { 2r - 1} - \frac { 2r } { 3r + 4}`?

Answer 1

`(-4r^2+8r+8)/((2r-1)(3r+4))` ( don't think this can be simplified any further)

Explanation:

First you need to find a common denominator. In this case that would be `(2r-1)(3r+4)`. To make them both have this denominator you would multiply the first term by `(3r+4)/(3r+4)` (which is the same as multiplying by 1), and you multiply the second term by `(2r-1)/(2r-1)`.
Now you have `(6r+8)/((2r-1)(3r+4)) -(4r^2-2r)/((2r-1)(3r+4))` which is equal to `(6r+8-4r^2+2r)/((2r-1)(3r+4))` `=(-4r^2+8r+8)/((2r-1)(3r+4))`