(3) / (x +1) + (1)/(x) / (2)/(x+1) + (3)/(x)?

Question

Simplify the complex fraction. Remember to include any changes in the domain.

Answer 1

(3) / (x +1) + (1)/(x) / (2)/(x+1) + (3)/(x)

Step 1: Simplify the numerator and denominator.
Numerator: 3/(x+1) + 1/x. To simplify, create a common denominator of x(x+1).
3/(x+1) * x/x + 1/x * (x+1)/x+1)
(3x + x + 1) / (x(x+1)
(4x + 1)/(x(x+1)

Denominator: 2/(x+1) + 3/x. To simplify, create a common denominator of x(x+1).
2/(x+1) * x/x + 3/x * (x+1)/x+1)
(2x +3x + 3) / (x(x+1)
(5x + 3)/(x(x+1)

Step 2: Put it back together and simplify.
((4x + 1)/(x(x+1)) / ((5x + 3)/(x(x+1))

Both parts have x(x+1) as a denomintor, so those cancel:
(4x + 1) / (5x + 3) (solution!)