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.

## 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

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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)

x

^{2}+2x = 8x - 8)Subtract 8x from each side

x

^{2}- 6x = -8Finally, add 8 to each side

x

^{2}- 6x + 8 = 0which 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

2x

^{2}- 2x = 3x + 122x

^{2}- 5x - 12 = 0which is a quadratic equation that can be factored into (x - 4)(2x + 3)

from which x = 4 or x = (-3/2)