Question 139559
{{{3/((3x-4))}}} + {{{2/((x-1))}}} = 2
:
Multiply equation by the common denominator; (3x-4)(x-1)
(3x-4)(x-1)*{{{3/((3x-4))}}} + (3x-4)(x-1*{{{2/((x-1))}}} = 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 = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
a=6; b=-23 c=19
{{{x = (-(-23) +- sqrt(-23^2 - 4 * 6 * 19 ))/(2*6) }}}
:
You should get two solutions:
x = 2.62867 and x = 1.20467