# Solving a Rational Inequality

• May 7th 2011, 07:34 AM
Punch
Solving a Rational Inequality
Using Analytical method, find the solution set of the inequality $\displaystyle \frac{3}{x-1}+\frac{5}{(x-2)^2} > \frac{3}{x-2}$
• May 7th 2011, 10:16 AM
TheEmptySet
Quote:

Originally Posted by Punch
Using Analytical method, find the solution set of the inequality \frac{3}{x-1}+\frac{5}{x-2}^2 > \frac{3}{x-2}

Getting a common denominator gives and moving everything to the right hand side gives

$\displaystyle 0 > \frac{3(x-1)-3(x+2)-5(x-1)}{(x-1)(x-2)}=\frac{-5x-4}{(x-1)(x-2)}$

So the inequality will change signs at

$\displaystyle x=1 \quad x=2 \quad x=-\frac{4}{5}$

can you finish from here?
• May 7th 2011, 10:51 PM
Punch
Thank you so much, but could u help me with one other thing? What does analytical method mean? i tried googling but only found definitions that i could not understand
• May 8th 2011, 06:53 AM
TheEmptySet
Quote:

Originally Posted by Punch
Thank you so much, but could u help me with one other thing? What does analytical method mean? i tried googling but only found definitions that i could not understand

Loosely speaking it means to find an exact solution using algebra calculus ect.

What it is saying is don't plot a graph and estimate ect.