SOLUTION: i have an urgent question i dont know how to do ratioal functios that have an = sign in them!!!!! Will you please show me how to work out these two problems???? my problems are: x

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Question 205151: i have an urgent question i dont know how to do ratioal functios that have an = sign in them!!!!! Will you please show me how to work out these two problems???? my problems are: x+1/2x = x-1/2x-1 and
2/m^2-3m-4 = 2/3m+12 - m/m-1
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
x+1/2x = x-1/2x-1
Cross multiply
(x+1)*(2x-1) = 2x*(x-1)
2x^2 + x - 1 = 2x^2 - 2x
x-1 = -2x
3x = 1
x = 1/3
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and
2/m^2+3m-4 = 2/3m+12 - m/m-1
2/(m^2+3m-4) = 2/(3(m+4)) - m/m-1
Are you sure the 1st term is not
2/(m^2+3m-4) ??
Poster confirmed via email that it's +, as below.
2/(m^2+3m-4) = 2/(3(m+4)) - m/m-1
2/(m+4)(m-1) = (2/3)/(m+4) - m/(m-1)
6/(m+4)(m-1) = 2/(m+4) - 3m/(m-1)
6/DEN = 2(m-1)/DEN - 3m(m+4)/DEN
6 = 2(m-1) - 3m(m+4)
6 = 2m-2 - 3m^2-12m
3m^2 + 10m + 8 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B10x%2B8+=+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=%2810%29%5E2-4%2A3%2A8=4.

Discriminant d=4 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-10%2B-sqrt%28+4+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2810%29%2Bsqrt%28+4+%29%29%2F2%5C3+=+-1.33333333333333
x%5B2%5D+=+%28-%2810%29-sqrt%28+4+%29%29%2F2%5C3+=+-2

Quadratic expression 3x%5E2%2B10x%2B8 can be factored:
3x%5E2%2B10x%2B8+=+%28x--1.33333333333333%29%2A%28x--2%29
Again, the answer is: -1.33333333333333, -2. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B10%2Ax%2B8+%29

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m = -2
m = -4/3