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

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) (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
-----------
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 (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=4 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: -1.33333333333333, -2. Here's your graph:

==========================================
m = -2
m = -4/3

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