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

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