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