SOLUTION: Hey there, how would u work this out X. 2 - - --- = 1 2. X+1

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Question 575593: Hey there, how would u work this out
X. 2
- - --- = 1
2. X+1
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
ok im going to guess u meant:
%28x%2F2%29-%28%282%29%2F%28x%2B1%29%29=1
instead of
x.2/(2.x+1)=1
.
%28x%2F2%29-%28%282%29%2F%28x%2B1%29%29=1
multiply by a number that will eliminate the denominators accross the equation
in this case the number is 2%28x%2B1%29
%282%28x%2B1%29%28x%2F2%29%29-%282%28x%2B1%29%29%28%282%29%2F%28x%2B1%29%29=1 use cross cancelation when distributing
%28x%2B1%29%28x%29-4=1 distribute the x
x%5E2%2Bx-4=1 put in quadratic formula
x%5E2%2Bx-5=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B1x%2B-5+=+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=%281%29%5E2-4%2A1%2A-5=21.

Discriminant d=21 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-1%2B-sqrt%28+21+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%281%29%2Bsqrt%28+21+%29%29%2F2%5C1+=+1.79128784747792
x%5B2%5D+=+%28-%281%29-sqrt%28+21+%29%29%2F2%5C1+=+-2.79128784747792

Quadratic expression 1x%5E2%2B1x%2B-5 can be factored:
1x%5E2%2B1x%2B-5+=+1%28x-1.79128784747792%29%2A%28x--2.79128784747792%29
Again, the answer is: 1.79128784747792, -2.79128784747792. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B1%2Ax%2B-5+%29