SOLUTION: (2+5/4x-1)= (-2/(4x-1)^2) I started it already but i do not really understand. This is what I have done: (2/1+5/4x-1)=(-2/(4x-1)^2) 2(4x-1)^2+5(4x-1)=-2 I do not know what else

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: (2+5/4x-1)= (-2/(4x-1)^2) I started it already but i do not really understand. This is what I have done: (2/1+5/4x-1)=(-2/(4x-1)^2) 2(4x-1)^2+5(4x-1)=-2 I do not know what else      Log On


   

Question 712487: (2+5/4x-1)= (-2/(4x-1)^2)
I started it already but i do not really understand. This is what I have done:
(2/1+5/4x-1)=(-2/(4x-1)^2)
2(4x-1)^2+5(4x-1)=-2
I do not know what else to do
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
(2+5/4x-1)= (-2/(4x-1)^2)
I started it already but i do not really understand. This is what I have done:
(2/1+5/4x-1)=(-2/(4x-1)^2)
2(4x-1)^2+5(4x-1)=-2
I do not know what else to do
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2%284x-1%29%5E2%2B5%284x-1%29=-2
2%2816x%5E2+-+8x+%2B+1%29+%2B+20x+-+5+=+-2
32x%5E2+-+16x+%2B+2+%2B+20x+-+5+=+-2
32x%5E2+%2B+4x+-+1+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 32x%5E2%2B4x%2B-1+=+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=%284%29%5E2-4%2A32%2A-1=144.

Discriminant d=144 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-4%2B-sqrt%28+144+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%284%29%2Bsqrt%28+144+%29%29%2F2%5C32+=+0.125
x%5B2%5D+=+%28-%284%29-sqrt%28+144+%29%29%2F2%5C32+=+-0.25

Quadratic expression 32x%5E2%2B4x%2B-1 can be factored:
32x%5E2%2B4x%2B-1+=+%28x-0.125%29%2A%28x--0.25%29
Again, the answer is: 0.125, -0.25. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+32%2Ax%5E2%2B4%2Ax%2B-1+%29

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You can check both, see if they work in the original equation.