Question 473479
{{{(x-2)/x = 4 - (x+4)/(x-3)}}}
Combine right side into 1 fraction: common denominator of (x-3)
{{{(x-2)/x = 4(x-3)/(x-3) - (x+4)/(x-3)}}}
{{{(x-2)/x = (4(x-3) - (x+4))/(x-3)}}}
{{{(x-2)/x = (4x -12 - x -4)/(x-3)}}}
{{{(x-2)/x = (3x -16)/(x-3)}}}
Cross-Multiply, this will get rid of fractions
{{{(x-2)(x-3) = x(3x-16)}}}
{{{x^2 - 5x +6 = 3x^2 - 16x}}}
Move everything to one side or set equation equal to zero.
{{{2x^2 - 11x - 6 = 0}}}
Solve quadratic by factoring or quadratic formula:
This factors, 2*-6 = -12 AND -12 + 1 = -11
{{{2x^2 -12x +x - 6 = 0}}}
{{{2x(x-6) + (x-6) = 0}}}
{{{(2x+1)(x-6) = 0}}}
2x+1=0 --> x = -1/2
x-6 =0 --> x = 6
Hope this helped