Question

How do you combine terms in (2/x) + (1/x+3) to get (3x+6)/(x^2+3x)?

Answer 1

you need a common denominator.

one way to get a common denominator is multiply the 2 denominators:
x(x+3)

now you need to multiply each fraction so you get that denominator.
for the first fraction, multiply by (x+3)/(x+3)
do you see what to multiply the 2nd fraction by to make its denominator x(x+3) ?

Answer 2

x/x?

Answer 3

yes

Answer 4

and I can do that because it's just 1 so I'm technically just multiplying by 1?

Answer 5

so you get
\[ \frac{2}{x}\frac{(x+3)}{(x+3)} + \frac{1}{(x+3)} \frac{x}{x} \]

yes, you are multiplying by 1 in each case,
now distribute the x in the bottom to get x^2+3x
up top, you can simplify

Answer 6

awesome! That makes so much sense now. Thanks!