Basic algebra denominator: simplify $\frac 1x+ \frac 12$

Question

I'm stuck wondering what to do with $\frac 1x+ \frac 12$

Is it $\frac{2+x}{2x}$ or $\frac{x+2}{2x}$...why?

Answer 1

To simplify $\frac{1}{x}+\frac{1}{2}$, we note that the common denominator is $2x$, thus

$\frac{1}{x}+\frac{1}{2} = \frac{2+x}{2x}$.

Answer 2

$$\frac{1}{x} + \frac{1}{2} = \frac{2}{2x} + \frac{x}{2x}$$

We have multiplied the first fraction's numerator and denominator by 2.

We have multiplied the second fraction's numerator and denominator by x.

$$\frac{2}{2x} + \frac{x}{2x} = \frac{2+x}{2x}$$

The two fractions you have put are actually equal to eachother.

You've got the answer right, don't worry!

Answer 3

Hint: $$\dfrac1x+\dfrac12=\dfrac12+\dfrac1x$$

and we may proceed as via Adam to get:

$$\dfrac{x+2}{2x}$$