Using Analytical method, find the solution set of the inequality $\displaystyle \frac{3}{x-1}+\frac{5}{(x-2)^2} > \frac{3}{x-2}$

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- May 7th 2011, 07:34 AMPunchSolving 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 AMTheEmptySet
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 PMPunch
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 AMTheEmptySet