So the expression is:
$$\frac1{2b} + \frac b2$$
Apparently the answer is $\frac{1 + b^2}{ 2b}$.
I came up with $2b$ by multiplying the first fraction by $2$ and the second fraction by $2b.$
I got: $$\frac{2+ 2b^2}{2(2b)}$$ which simplifies to $\frac{2b^2}{2b}$ which is where I got $2b$ from. Can someone help me with this problem and the LCD?
If you have
$$ \frac{1}{2b}+\frac{b}{2} $$
the LCD of the denominators is $2b$; therefore, the first fraction can be left alone, and the second fraction multiplied by $b/b$ to yield
$$ \frac{1}{2b}+\frac{b^2}{2b} $$
which can then be combined to obtain
$$ \frac{1+b^2}{2b} $$
It seemed to me, incidentally, that you obtained
$$ \frac{2+2b^2}{2(2b)} $$
which wants only division by $2/2$ to get
$$ \frac{1+b^2}{2b} $$
as above. As a side note, I would say that writing out fractions "in-line" as opposed to "stacked" (as it were) makes it potentially confusing just exactly where the numerators and denominators begin and end. I don't know if you're doing that as you work out the problem, but if you are, it might lead to errors.