SOLUTION: what are the zeros to the function : (3/3x-4) + (2/x-1) = 2

Algebra ->  Rational-functions -> SOLUTION: what are the zeros to the function : (3/3x-4) + (2/x-1) = 2      Log On


   

Question 139559: what are the zeros to the function :
(3/3x-4) + (2/x-1) = 2
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
3%2F%28%283x-4%29%29 + 2%2F%28%28x-1%29%29 = 2
:
Multiply equation by the common denominator; (3x-4)(x-1)
(3x-4)(x-1)*3%2F%28%283x-4%29%29 + (3x-4)(x-1*2%2F%28%28x-1%29%29 = 2(3x-4)(x-1)
;
Cancel out the denominators, FOIL on the right
3(x-1) + 2(3x-4) = 2(3x^2 - 7x + 4)
:
Multiply what's inside the brackets:
3x - 3 + 6x - 8 = 6x^2 - 14x + 8
;
9x - 11 = 6x^2 - 14x + 8
:
Combine on the right:
0 = 6x^2 - 14x - 9x + 8 + 11
:
A quadratic equation:
6x^2 - 23x + 19 = 0
:
To find the 0's use the quadratic formula:x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a=6; b=-23 c=19
x+=+%28-%28-23%29+%2B-+sqrt%28-23%5E2+-+4+%2A+6+%2A+19+%29%29%2F%282%2A6%29+
:
You should get two solutions:
x = 2.62867 and x = 1.20467