Q: Condense: 3/2x + x/(2x-6)
In order to add fractions, we need to have common denominators. Remember, in order to get common denominators, we need to multiply by something.. Just because one denominator is 2x – 6 and the other is 2x, we cannot just subtract 6 to make them match.
So, the fraction on the left needs a (2x-6) and the fraction on the right needs a (2x)… So, you have to multiply the fraction on the left by (2x-6) and the fraction on the right needs to be multiplied by (2x). Remember: multiply to the top and the bottom like so:
3/2x + x/(2x-6)
3(2x-6)/2x(2x-6) + x(2x)/(2x-6)(2x)
Now, simplify each numerator, leave the denominators alone: