Question

Algebra question

Answer 1

I have the following equation

Answer 2

I need to solve for W/C0*V0*p

Answer 3

Basically, I am subtracting 1/c0 from both sides, dividing by t and then multiplying both sides by -1

Answer 4

I am given values for these variables and then the solution, but the numbers dont add up for me. Any ideas?

Answer 5

\[\large\begin{align*}\frac{1}{c}&=\frac{1}{c_0}-\frac{W}{c_0V_0\rho_w}t\\\\
\frac{1}{c}-\frac{1}{c_0}&=-\frac{W}{c_0V_0\rho_w}t\\\\
-\frac{1}{c}+\frac{1}{c_0}&=\frac{W}{c_0V_0\rho_w}t\\\\
\frac{1}{c_0}-\frac{1}{c}&=\frac{W}{c_0V_0\rho_w}t\\\\
\frac{1}{t}\left(\frac{1}{c_0}-\frac{1}{c}\right)&=\frac{W}{c_0V_0\rho_w}\\\\
\frac{1}{c_0t}-\frac{1}{ct}&=\frac{W}{c_0V_0\rho_w}\end{align*}\]
You may elect to combine the fractions on the left side.

Answer 6

It looks like they do exactly that, so you'd have
\[\large\begin{align*}\frac{1}{c_0t}-\frac{1}{ct}&=\frac{W}{c_0V_0\rho_w}\\\\
\frac{c}{c_0ct}-\frac{c_0}{c_0ct}&=\frac{W}{c_0V_0\rho_w}\\\\
\frac{c-c_0}{c_0ct}&=\frac{W}{c_0V_0\rho_w}\end{align*}\]
Notice that there's a factor of \(c_0\) in both denominators, so you can elminate them:
\[\large\frac{c-c_0}{ct}=\frac{W}{V_0\rho_w}\]

Answer 7

How did you inverse the fraction?

Answer 8

I mean, c and c0 are numerators all of sudden.

Answer 9

@SithsAndGiggles I think I am missing something obvious here!

Answer 10

Sorry, was away for a bit.

What I did was find a common denominator. It's a common method you would use to find the difference between two fractions. Here's an example,
\[\frac{1}{2}-\frac{1}{4}\]
We want a 4 in both denominators, so what can we do? We multiply the first fraction by 2/2, because then
\[\frac{1}{2}\cdot\frac{2}{2}=\frac{2}{4}\]
(we multiply by 2/2 because 2/2=1, and multiplying anything by 1 doesn't change its value).
So we have
\[\frac{2}{4}-\frac{1}{4}=\frac{2-1}{4}-\frac{1}{4}\]

Answer 11

\[\large\begin{align*}\frac{1}{c_0t}-\frac{1}{ct}&=\frac{W}{c_0V_0\rho_w}\\\\
\frac{\color{red}c}{c_0\color{red}ct}-\frac{\color{red}{c_0}}{\color{red}{c_0}ct}&=\frac{W}{c_0V_0\rho_w}\\\\
\frac{c-c_0}{c_0ct}&=\frac{W}{c_0V_0\rho_w}\end{align*}\]

Answer 12

You're basically just multiplying both fractions by c/c and c0/c0 respectively so that you can simply in next step

Answer 13

Correct, doing so makes both denominators the same, so I can combine the fractions and simplify.

Answer 14

Thank you for the help. I have been staring at this problem for a while!

Answer 15

You're welcome!