# How does this differential simplify

How does the following differential from the first line become equal to the second line ?

This is confusing me as I do not know where the 3 has come from.

• $1 + 1/2 = 3/2$ – eyeballfrog Aug 13 at 23:22
• What worries me is that it looks like the $e^{-x/2}$ became $e^{-x/3}$. – Gerry Myerson Aug 13 at 23:46
• Yes that’s true must be a mistake – Dan Aug 13 at 23:57

## 1 Answer

Isolate $$e^{-x/2}$$
Then you have $$e^{-x/2}(-1 - \frac{1}{2}+\frac x2) = e^{-x/2}(-\frac32+\frac x2) = \frac{1}{2}e^{-x/2}(x-3)$$

• Thank you I understand now – Dan Aug 13 at 23:25
• You're welcome! – Ak19 Aug 13 at 23:27