# Thread: Need help simplifying some expressions!

1. ## Need help simplifying some expressions!

Ok, I have a couple of expressions that I need to put in terms of X (and only X), where X=(A-B)/A. I have listed them below...I know that this should be relatively simple but I seem to be having alot of trouble with this. Could anyone please show/explain how to go about simplifying these expressions? Thanks a bunch in advance!

Expression 1: (B)/((3*A)-(2*B))
Expression 2: (2*(A-B))/((3*A)-(2*B))
Expression 3: (A-B)/((3*A)-(2*B))
Expression 4: ((-.5*A)-B)/((.5*A)-B)

2. ## Re: Need help simplifying some expressions!

Expression 1: $\frac{B}{3A-2B}$
And because $x=\frac{A-B}{A} \Rightarrow x=1-\frac{B}{A} \Rightarrow \frac{B}{A}=1-x \Rightarrow B=A-Ax \ \mbox{and} \ A=\frac{B}{1-x}$
Therefore you can write expression 1 as:
$\frac{A-Ax}{\frac{3B}{1-x}-2A+2Ax}=\frac{A-Ax}{\frac{3A-3Ax}{1-x}-2A+2Ax}=\frac{A(1-x)}{A\left[\left(\frac{3-3x}{1-x}\right)-2+2x\right]}=...$

Try to do something similar for the other expressions.