# Thread: Simplify expression, isolating Q

2. ## Re: Simplify expression, isolating Q

Hey mrtn.

Hint: Take the -dS/Q^2 term to the RHS side and then take the reciprocal of both sides which will give Q^2/dS = blah. After this you multiply both sides by dS and take the square root.

Show us your attempts so we can guide you through them.

3. ## Re: Simplify expression, isolating Q

Originally Posted by mrtn

Question: What is the subscript on h for?

I would move the fraction with Q^2 to the right hand side of the equation to start.

$\displaystyle \frac{h}{2} - \frac{dh}{2p} = \frac{ dS}{Q^2}$

Combine fractions on the left

$\displaystyle \frac{h(p - d)}{2p} = \frac{dS}{Q^2}$

Divide both terms in the parenthesis by p

$\displaystyle \frac{h(1 - \frac{d}{p})}{2} = \frac{Q^2}{dS}$

Invert both sides

$\displaystyle \frac{2}{h(1 - \frac{d}{p})} = \frac{Q^2}{dS}$

Multiply by dS

$\displaystyle \frac{2Sd}{h(1 - \frac{d}{p})} = Q^2$

Extract the root

$\displaystyle Q = \pm \sqrt{\frac{2Sd}{h(1 - \frac{d}{p})}}$

Question: What is the subscript on h for?

4. ## Re: Simplify expression, isolating Q

Hey chiro.

This is what I can come up with:

I still cant get there.

Sorry about the h / hl thing - they are the same

5. ## Re: Simplify expression, isolating Q

Originally Posted by mrtn
Hey chiro.

This is what I can come up with:

I still cant get there.

Sorry about the h / hl thing - they are the same
You cannot invert before you combine because it doesn't work COMBINE FIRST , then invert.

$\displaystyle 2 + 3 = 5$ but $\displaystyle \frac{1}{2} + \frac{1}{3} \ne \frac{1}{5}$