SOLUTION: can you help me solve this problem {{{ (10/x)+3=(x+9)/(x-4) }}}

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Question 591554: can you help me solve this problem +%2810%2Fx%29%2B3=%28x%2B9%29%2F%28x-4%29+
Answer by mananth(12270) About Me  (Show Source):
You can put this solution on YOUR website!
+%2810%2Fx%29%2B3=%28x%2B9%29%2F%28x-4%29+

+%2810%2Fx%29-%28%28x%2B9%29%2F%28x-4%29%29+=-3

The LCD = x(x-4)
multiply equation by the LCD
10(x-4) -x(x+9) = -3x(x-4)

10x-40-x%5E2-9x=-3x%5E2%2B12x

x-40-x%5E2=-3x%5E2%2B12x

3x%5E2-x%5E2%2Bx-12x-40=0

2x%5E2-11x-40=0

2x%5E2-16x%2B5x-40=0

2x%28x-8%29%2B5%28x-8%29=0
(x-8)(2x+5)=0

x= 8 Or x= -5/2