Question 3984
{{{(x+4)/(6x^2+5x-6) + x/(2x+3) = x/(3x-2)}}}

{{{(x+4)/((3x-2)(2x+3)) + x/(2x+3) = x/(3x-2)}}}


Now multiply every term by (3x-2)(2x+3):


{{{((x+4)(3x-2)(2x+3))/((3x-2)(2x+3)) + x((3x-2)(2x+3))/(2x+3) = x((3x-2)(2x+3))/(3x-2)}}}


Now we can cancel terms:


{{{(x+4) + x(3x-2) = x(2x+3)}}}

{{{x+4 + 3x^2-2x = 2x^2+3x}}}

{{{x^2 - 4x + 4 = 0}}}


(x-2)(x-2) = 0


so x=2.


I haven't checked, but put x=2 into the original Righthand side and lefthand side and the answer should be the same number.


jon.