If M = S, how to isolate a?

Question

So I have to isolate $a$ in $M=S$

$M=1+\dfrac{a}{b}$

$S=a+b$

So, I put it up like this:

$1+\dfrac{a}{b}=a+b$

... right?

But then what?

Answer 1

You have

$$1+\frac a b=a+b\iff a\left(\frac1b-1\right)=b-1\iff a\frac{1-b}{b}=b-1$$ hence

• if $b=1$ then the equality is true for all $a$
• and if $b\ne 1$ then $a=-b$ for $b\ne0$.