Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Solve by using sign charts and express the solutions in interval form.

$$\text{(a)} \frac{(x+2)(x-3)^{2}}{x^{2}+x-2} \geq 0$$ $$\text{(b)} \frac{1}{x-1} < \frac{2}{x}$$

share|cite|improve this question
Is there a certain part you're having trouble with? Typically, full answers are not provided for homework questions, just helpful hints when you get stuck. It would be to your advantage to show any work you've done thus far, or explain why you're having difficulty. – user80696 Jun 4 '13 at 21:33

Here is a full solution for $(b)$

$$ \frac{1}{x-1} < \frac{2}{x} \implies \frac{2}{x} - \frac{1}{x-1}>0 \implies \frac{x-2}{x(x-1)}>0 $$

$$ \implies \left\{x-2>0\quad \cap \quad x(x-1)>0 \right\} \cup \left\{x-2<0\quad \cap \quad x(x-1)<0 \right\} $$

$$ \implies \left\{x-2>0\, \cap\,(x-1)>0 \right\}\cup \left\{x-2<0\,\cap\left\{( x<0 \cap x-1>0 ) \cup ( x>0 \cap x-1<0 )\right\}\right\} $$

$$ \implies \left\{x-2 >0 \right\} \cup \left\{ x-2<0 \,\cap \, 0<x<1 \right\} $$

$$ \implies \left\{x-2 >0 \right\} \cup \left\{ 0<x<1 \right\} $$

$$ \implies (2,\infty) \cup ( 0,1 ) $$

Note: $\cup$ stands for union while $\cap$ stands for intersection.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.