SOLUTION: (3/2m+4)=(1/m+2)-2 Thankyou.

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Question 50101: (3/2m+4)=(1/m+2)-2
Thankyou.
Found 2 solutions by stanbon, Roric:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
(3/2m+4)=(1/m+2)-2
(3/2(m+2))= 1/(m+2)-2
Multiply thru by 2(m+2) to get:
3 = 2-(m+2)
1=-m-2
m=-3
Cheers,
Stan H.

Answer by Roric(1) About Me  (Show Source):
You can put this solution on YOUR website!
For this question, we need to solve the equation for the value of m. To do this, we must get m alone. The parenthesis in the equation are irrelavent and confusing, so lets get rid of them. (3/2)m + 4 = 1/m + 2 - 2
The +2-2 cancels out, leaving us with (3/2)m + 4 = 1/m. Next we multiply the entire equation by m in order to get rid of the m in the denominator.
m((3/2)m + 4) = m(1/m) -->(3/2)m^2 + 4m = 1 --> (3/2)m^2 + 4m - 1 = 0.
We can now use the quadratic equation to solve for m.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation am%5E2%2Bbm%2Bc=0 (in our case 1.5m%5E2%2B4m%2B-1+=+0) has the following solutons:

m%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=%284%29%5E2-4%2A1.5%2A-1=22.

Discriminant d=22 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-4%2B-sqrt%28+22+%29%29%2F2%5Ca.

m%5B1%5D+=+%28-%284%29%2Bsqrt%28+22+%29%29%2F2%5C1.5+=+0.23013858660781
m%5B2%5D+=+%28-%284%29-sqrt%28+22+%29%29%2F2%5C1.5+=+-2.89680525327448

Quadratic expression 1.5m%5E2%2B4m%2B-1 can be factored:
1.5m%5E2%2B4m%2B-1+=+1.5%28m-0.23013858660781%29%2A%28m--2.89680525327448%29
Again, the answer is: 0.23013858660781, -2.89680525327448. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1.5%2Ax%5E2%2B4%2Ax%2B-1+%29