SOLUTION: 2/x-4/(x+1)=3

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Question 214660: 2/x-4/(x+1)=3
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
2%2Fx-4%2F%28x%2B1%29=3

Step 1. Multiply by x(x+1) to both sides to get rid of denominators.

x%28x%2B1%29%2A%282%2Fx-4%2F%28x%2B1%29%29=x%28x%2B1%293

Step 2. Simplify above equation

2%28x%2B1%29-4x=3x%5E2%2B3x

3x%5E2%2B3x=2x%2B2-4x=-2x%2B2

3x%5E2%2B3x%2B2x-2=-2x%2B2%2B2x-2=0

3x%5E2%2B5x-2=0

Step 3. We can then use the quadratic formula to solve the above equation given as x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

where a=3, b=5, and c=-2

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B5x%2B-2+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%285%29%5E2-4%2A3%2A-2=49.

Discriminant d=49 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-5%2B-sqrt%28+49+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%285%29%2Bsqrt%28+49+%29%29%2F2%5C3+=+0.333333333333333
x%5B2%5D+=+%28-%285%29-sqrt%28+49+%29%29%2F2%5C3+=+-2

Quadratic expression 3x%5E2%2B5x%2B-2 can be factored:
3x%5E2%2B5x%2B-2+=+3%28x-0.333333333333333%29%2A%28x--2%29
Again, the answer is: 0.333333333333333, -2. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B5%2Ax%2B-2+%29



Step 4. ANSWER: The solutions are 1%2F3 and -2

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J