Q: Add x/(x+1) + 2x/(x+1)
also, identify any x-values for which the expression is undefined.
Answer: In order to add rational expressions, you need common denominators. These expressions already have a common denominator of (x+1) so the hard work is done.
You can just add the numerators together and combine the fraction (leave the denominator alone) to get:
x/(x+1) + 2x/(x+1) = (x + 2x) /(x+1) = 3x / (x + 1) [final answer]
Now, we need to identify any x-values for which the expression is undefined. We need to know that you can never divide by 0, so the denominator of any rational expression can never equal 0.
So, look at the denominator and find where it equals 0:
x+1 = 0
Solve for x to get:
x = -1
Therefore, the denominator is 0 if x = -1. This tells us that x can never be -1. The problem is undefined when x = -1.