precalculus problem, please help!?

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solve the nonlinear inequality and express in interval notation

[3/(x-1)] – [4/x] > 1

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A few days ago

hayharbr

Favorite Answer

First assume it’s equal to 1. Multiply all parts by the common denominator which is (x-1)(x), which cancels out the denominators. Leaves this:

3(x) – 4(x-1) = 1(x)(x-1)

3x – 4x + 4 = x^2 – x

-1x + 4 = x^2 – 1x

4 = x^2

x = 2 or -2

Now try numbers less than -2, greater than 2, and in between in the original inequality to see which work.

Say you try x = 4; 3/3 – 4/4 > 1; 0-0 > 1, false

try x = -4; 3/-5 – 4/-4 > 1; – 3/5 + 1 > 1 false

try -1: 3/-2 – 4/-1 > 1; -3/2 + 4 > 1 true

So the answer is -2 < x < 2; x is not equal to 1 or 0 [since it's undefined there]

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