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Hi, I need help with this certain problem based on solving equations with fractions. 1st problem) x/x-1 = 8/x+2 2nd problem) 2x/x+4 = 3/x-1

I don't know how to start it off with both of these problems. Please help me ASAP, this homework is due at 12 AM tonight! Please and thank you.
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1 Answer

Dear Lisa,
 
OK, let's solve these nasty problems.
 
1. [x/(x - 1)] = [8/(x + 2)]
 
Multiply both sides by (x - 1)
 
x = [8(x - 1)/(x+2)]
 
Now multiply both sides by (x + 2)
 
x(x + 2) = 8(x - 1)
 
x2 +2x = 8x - 8)
 
Subtract 8x from each side
 
x2 - 6x = -8
 
Finally, add 8 to each side
 
x2 - 6x + 8 = 0
 
which has the familiar look of a quadratic equation.  This one can be factored into
 
(x - 2)x - 4) = 0
 
from which x = 2 or x = 4
 
2.  [2x/(x + 4)] = [3/(x - 1)]
 
Same idea as before.  Multiply by (x + 4)
 
2x = [3(x + 4)/(x - 1)]
 
Multiply by (x - 1):
 
2x(x - 1) = 3x + 12
 
2x2 - 2x = 3x + 12
 
2x2 - 5x - 12 = 0
 
which is a quadratic equation that can be factored into (x - 4)(2x + 3)
 
from which x = 4 or x = (-3/2)