Replacing a combination of terms

Question

I have a quite simple question. I have an expression that looks similar to $T=\frac{1}{a_1}-\frac{1}{a_2}+1$ and I'd like Mathematica to use $A=\frac{a_1}{a_2}$ to reformat the expression (if possible) such that only $A$ appears in it.

Any idea?

Cheers, Pascal

Answer 1

Here is your expression and a rule for replacement:

T = 1/a1 - 1/a2;
rule = a1 -> A*a2;

Let us replace:

T /. rule

You get this:

-(1/a2) + 1/(A a2)

You may further transform it. For example:

% // Factor

The result is:

-((-1 + A)/(A a2))