Question

How/why does
[(1/2)e^(2x)] {- [x/(2x + 1)] + (1/2)}
simplify to
[(1/2)e^(2x)] {(- 2x + 2x + 1) /[2(2x + 1)]}
?

Answer 1

simplification
- x/(2x + 1) + (1/2)

Answer 2

Yeah I understand it simplifies but how does that happen? I bet its really obvious but I don't understand what happens between steps

Answer 3

\[ -\frac{ x}{(2x + 1)} + \frac{1}{2} \]
multiply the first fraction by 2/2 and the second by (2x+1)/(2x+1) to get a common denominator of 2(2x+1):
\[ \frac{2}{2} \cdot\frac{-x}{(2x+1)}+\frac{1}{2}\cdot \frac{(2x+1)}{(2x+1)}\]
\[ \frac{-2x}{2(2x+1)}+ \frac{(2x+1)}{2(2x+1)}\]
\[ \frac{-2x+2x+1}{2(2x+1)} \]
which becomes
\[ \frac{1}{2(2x+1)} \]

Answer 4

Thanks!