Suppose we wish to solve the following problem:
2x/(x + 1) + 3/x = 12
First we need to get a common denominator. Notice the factors in the denominators are (x+1) for the first term and x for the second term. We multiply the factors to get x(x+ 1) for the common denominator.
The numerator and denominator of the first term is multiplied by x and the numerator and denominator of the second term is multiplied by (x + 1). The 12 is multiplied by x(x + 1)/x(x + 1).
This gives us
2x(x)/x(x+1) + 3(x+ 1)/x(x + 1) = 12x(x + 1)/x(x + 1)
When solving this, we can ignore the denominators. The resason for this is since all the denominators are the same, we can multiply the entire equation by x(x + 1), which cancels the denominators
This leaves us with
2x(x) + 3(x + 1) = 12x(x + 1)
2x^2 + 3x + 3 = 12x^2 + 12x
0 = 10x^2 + 9x - 3
Using quadratic formula we get
x = [(-9 +/- sqrt(81- 4(10)(-3))]/2(10)
x = [-9 +/- sqrt(201)]/20
Solving for x, we get x is approximately 0.259 or -1.16