SOLUTION: How do you solve {{{ 6 -(5/(x+1)) = (6/(x-3))}}} I have tried this problem, but I go nowhere. {{{(6x+6-5)/(x+1) = (-6/(x-3))}}} {{{6(x+1)/(x+1) - 5/(x+1)}}}

Algebra ->  Rational-functions -> SOLUTION: How do you solve {{{ 6 -(5/(x+1)) = (6/(x-3))}}} I have tried this problem, but I go nowhere. {{{(6x+6-5)/(x+1) = (-6/(x-3))}}} {{{6(x+1)/(x+1) - 5/(x+1)}}}      Log On


   

Question 985255: How do you solve +6+-%285%2F%28x%2B1%29%29+=+%286%2F%28x-3%29%29
I have tried this problem, but I go nowhere.
%286x%2B6-5%29%2F%28x%2B1%29++=++%28-6%2F%28x-3%29%29
6%28x%2B1%29%2F%28x%2B1%29+-+5%2F%28x%2B1%29
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
How do you solve +6+-%285%2F%28x%2B1%29%29+=+%286%2F%28x-3%29%29
I have tried this problem, but I go nowhere.
%286x%2B6-5%29%2F%28x%2B1%29++=++-6%2F%28x-3%29 *** This is OK, except you changed the RHS to negative.
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%286x%2B6-5%29%2F%28x%2B1%29++=++6%2F%28x-3%29
%286x%2B1%29%2F%28x%2B1%29++=++6%2F%28x-3%29
Cross multiply
6(x+1) = (6x+1)*(x-3)
6x+%2B+6+=+6x%5E2+-+17x+-+3
6x%5E2+-+23x+-+9+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 6x%5E2%2B-23x%2B-9+=+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=%28-23%29%5E2-4%2A6%2A-9=745.

Discriminant d=745 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--23%2B-sqrt%28+745+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-23%29%2Bsqrt%28+745+%29%29%2F2%5C6+=+4.19122401065936
x%5B2%5D+=+%28-%28-23%29-sqrt%28+745+%29%29%2F2%5C6+=+-0.35789067732603

Quadratic expression 6x%5E2%2B-23x%2B-9 can be factored:
6x%5E2%2B-23x%2B-9+=+%28x-4.19122401065936%29%2A%28x--0.35789067732603%29
Again, the answer is: 4.19122401065936, -0.35789067732603. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+6%2Ax%5E2%2B-23%2Ax%2B-9+%29