SOLUTION: How would you solve the equation by factoring? {{{ 4(x-2)/(x-3)+3/x=(-3)/x(x-3) }}}

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: How would you solve the equation by factoring? {{{ 4(x-2)/(x-3)+3/x=(-3)/x(x-3) }}}      Log On


   

Question 491476: How would you solve the equation by factoring? +4%28x-2%29%2F%28x-3%29%2B3%2Fx=%28-3%29%2Fx%28x-3%29+
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

+4%28x-2%29%2F%28x-3%29%2B3%2Fx=%28-3%29%2Fx%28x-3%29+...common denominator is x%28x-3%29+

+4x%28x-2%29%2Fx%28x-3%29%2B3%28x-3%29%2Fx%28x-3%29=%28-3%29%2Fx%28x-3%29+

+%284x%28x-2%29%2B3%28x-3%29%29%2Fx%28x-3%29=%28-3%29%2Fx%28x-3%29+

+%284x%5E2-8x%2B3x-9%29%2Fcross%28x%28x-3%29%29=%28-3%29%2Fcross%28x%28x-3%29%29+

+4x%5E2-8x%2B3x-9=-3+

+4x%5E2-5x-9%2B3=0+

+4x%5E2-5x-6=0+
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

x+=+%28-%28-5%29+%2B-+sqrt%28+%28-5%29%5E2-4%2A4%2A%28-6%29+%29%29%2F%282%2A4%29+

x+=+%285+%2B-+sqrt%2825%2B96%29%29%2F8+

x+=+%285+%2B-+sqrt%28121%29%29%2F8+

x+=+%285+%2B-+11%29%2F8+
solutions:
x+=+%285+%2B+11%29%2F8+
x+=+16%2F8+
highlight%28x+=2%29+
or
x+=+%285-+11%29%2F8+
x+=+-6%2F8+
x+=highlight%28-3%2F4%29+