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I am doing a problem set and have several formulas that are quite ugly such as $$b=\left(\frac{3p_b}{2p_r}\right)^{\frac{1}{\rho-1}} \left(\frac{m}{p_r + p_b \left(\frac{3p_b}{2p_r}\right)^{\frac{1}{\rho-1}} }\right)$$ To see if any of them can be simplified, I plug them into Wolfram Alpha and check. But that's not going to work on a test. I need someway to quickly check if a given expression can be simplified.

Any suggestions on this issue?

Stan Shunpike
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1 Answers1

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$$b=\left(\frac{3p_b}{2p_r}\right)^{\frac{1}{\rho-1}} \left(\frac{m}{p_r + p_b \left(\frac{3p_b}{2p_r}\right)^{\frac{1}{\rho-1}} }\right)=$$ $$= \frac{m\left(\frac{3p_b}{2p_r}\right)^{\frac{1}{\rho-1}}}{p_r + p_b \left(\frac{3p_b}{2p_r}\right)^{\frac{1}{\rho-1}} }=$$ $$= \frac{m}{p_r\left(\frac{3p_b}{2p_r}\right)^{\frac{1}{1-\rho}} + p_b }.$$

Does this look simpler?

zoli
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  • Yes, I should have tried substituting a variable $c$ in place. That would have been obvious had I done that. Smart! – Stan Shunpike Apr 17 '15 at 23:38
  • But I'm more just concerned with that...every time I have to simplify, I use wolfram alpha. I mean, its not bad for multiplication addition, etc but the exponents get me confused. – Stan Shunpike Apr 17 '15 at 23:38
  • The unnecessary large brackets were also confusing. – zoli Apr 17 '15 at 23:42
  • Oh, that's because I had to plug stuff in. It was how I kept it clear in my head where I needed to copy and paste the latex. But I see your point – Stan Shunpike Apr 17 '15 at 23:50
  • I wish I could keep my head clean. Brackets don't help : ) – zoli Apr 17 '15 at 23:51