Question

How do you simplify `\frac { m ^ { 2} - n ^ { 2} + ( m + n ) ^ { 2} } { 2m }`?

Answer 1

`m+n`

Explanation:

Here's what we start with:
`(m^2-n^2+(m+n)^2)/(2m)`

We'll get rid of the square by multiplying `(m+n)` by `(m+n)`
`(color(red)(m^2)-color(green)(n^2)+color(red)(m^2)+2mn+color(green)(n^2))/(2m)`

Now, we can combine like terms.
`(2m^2+2mn)/(2m)`

Lastly, we can reduce the fraction.
`(color(red)(2m)^2+color(red)(2m)n)/(color(red)(2m))`

This leaves us with:
`m+n`