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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.

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)