How do you combine 1/2+2/(x+2)?

Nov 14, 2016

$\frac{x + 6}{2 x + 4}$

Explanation:

A fraction consists of

$\left(\text{numerator")/("denominator") -> ("count")/("size indicator of what you are counting}\right)$

$\textcolor{b l u e}{\text{Important fact 1}}$
You can not DIRECTLY add or subtract the counts unless the size indicators are the same

$\textcolor{b l u e}{\text{Important fact 2}}$
Multiply by 1 and you do not change the value. However, 1 comes in many forms so you can change the way numbers look but not change their actual value.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
color(blue)([1/2color(red)(xx1)]+[2/(x+2)color(red)(xx1)]

Is the same as:

color(blue)([1/2color(red)(xx(x+2)/(x+2))]+[2/(x+2)color(red)(xx2/2)]

$\frac{x + 2}{2 \left(x + 2\right)} + \frac{4}{2 \left(x + 2\right)}$

$\frac{x + 2 + 4}{2 \left(x + 2\right)} \text{ "=" } \frac{x + 6}{2 x + 4}$