SOLUTION: Solve the rational equation: {{{ (2)/(3x-1)- (x)/(x+1)=0 }}}

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Solve the rational equation: {{{ (2)/(3x-1)- (x)/(x+1)=0 }}}       Log On


   

Question 363394: Solve the rational equation: +%282%29%2F%283x-1%29-+%28x%29%2F%28x%2B1%29=0+
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
(2)/(3x-1)- (x)/(x+1)=0
2(x+1)-x(3x-1)=0
2x+2-3x^2+x=0
-3x^2+3x+2=0
x=(3-sqrt(33))/6, x=(3+sqrt(33))/6
.
Ed
.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -3x%5E2%2B3x%2B2+=+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=%283%29%5E2-4%2A-3%2A2=33.

Discriminant d=33 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-3%2B-sqrt%28+33+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%283%29%2Bsqrt%28+33+%29%29%2F2%5C-3+=+-0.457427107756338
x%5B2%5D+=+%28-%283%29-sqrt%28+33+%29%29%2F2%5C-3+=+1.45742710775634

Quadratic expression -3x%5E2%2B3x%2B2 can be factored:
-3x%5E2%2B3x%2B2+=+-3%28x--0.457427107756338%29%2A%28x-1.45742710775634%29
Again, the answer is: -0.457427107756338, 1.45742710775634. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-3%2Ax%5E2%2B3%2Ax%2B2+%29