SOLUTION: 3x-5/x+2=x-1/2x-1 6x^2-13x+5=x^2+x-2 5x^2-14x+7 -(-14)+or-sqrt(-14)^2-4(5)(7)/2(5) 14+or-sqrt196-140/10 14+or-sqrt56/10 14+or-2sqrt14/5 I know I am doing this wrong. I wou

Algebra ->  Rational-functions -> SOLUTION: 3x-5/x+2=x-1/2x-1 6x^2-13x+5=x^2+x-2 5x^2-14x+7 -(-14)+or-sqrt(-14)^2-4(5)(7)/2(5) 14+or-sqrt196-140/10 14+or-sqrt56/10 14+or-2sqrt14/5 I know I am doing this wrong. I wou      Log On


   

Question 282913: 3x-5/x+2=x-1/2x-1
6x^2-13x+5=x^2+x-2
5x^2-14x+7
-(-14)+or-sqrt(-14)^2-4(5)(7)/2(5)
14+or-sqrt196-140/10
14+or-sqrt56/10
14+or-2sqrt14/5
I know I am doing this wrong. I would greatly appreciate some direction. Thank you and I look forward to finding out where I went wrong.
Tina
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%283x-5%29%2F%28x%2B2%29=%28x-1%29%2F%282x-1%29 Start with the given equation.


%283x-5%29%282x-1%29=%28x%2B2%29%28x-1%29 Cross multiply


6x%5E2-13x%2B5=x%5E2%2Bx-2 FOIL


6x%5E2-13x%2B5-x%5E2-x%2B2=0 Get every term to the left side.


5x%5E2-14x%2B7=0 Combine like terms.


Notice that the quadratic 5x%5E2-14x%2B7 is in the form of Ax%5E2%2BBx%2BC where A=5, B=-14, and C=7


Let's use the quadratic formula to solve for "x":


x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


x+=+%28-%28-14%29+%2B-+sqrt%28+%28-14%29%5E2-4%285%29%287%29+%29%29%2F%282%285%29%29 Plug in A=5, B=-14, and C=7


x+=+%2814+%2B-+sqrt%28+%28-14%29%5E2-4%285%29%287%29+%29%29%2F%282%285%29%29 Negate -14 to get 14.


x+=+%2814+%2B-+sqrt%28+196-4%285%29%287%29+%29%29%2F%282%285%29%29 Square -14 to get 196.


x+=+%2814+%2B-+sqrt%28+196-140+%29%29%2F%282%285%29%29 Multiply 4%285%29%287%29 to get 140


x+=+%2814+%2B-+sqrt%28+56+%29%29%2F%282%285%29%29 Subtract 140 from 196 to get 56


x+=+%2814+%2B-+sqrt%28+56+%29%29%2F%2810%29 Multiply 2 and 5 to get 10.


x+=+%2814+%2B-+2%2Asqrt%2814%29%29%2F%2810%29 Simplify the square root


x+=+%2814%2B2%2Asqrt%2814%29%29%2F%2810%29 or x+=+%2814-2%2Asqrt%2814%29%29%2F%2810%29 Break up the expression.


x+=+%287%2Bsqrt%2814%29%29%2F%285%29 or x+=+%287-sqrt%2814%29%29%2F%285%29 Reduce.


So the solutions are x+=+%287%2Bsqrt%2814%29%29%2F%285%29 or x+=+%287-sqrt%2814%29%29%2F%285%29


So it looks like you're on the right track.