Question

Solve for c in this equation a(b-c)=a/b

Answer 1

The problem is asking us to isolate $c$. This means that we are going to want to get $c$ on its own side, with no other variables or terms. We can see that there is both an $a$ and $b$ on the side of the equation with $c$, so our goal will be to remove those.

To get rid of the $a$, let's divide both sides of the equation by $a$. This gives us:

$\dfrac{a (b - c)}{a} = \dfrac{\frac{a}{b}}{a}$

$(b - c) = \dfrac{a}{b} \cdot \dfrac{1}{a} = \dfrac{1}{b}$

$(b - c) = \dfrac{1}{b}$

Now, we are still going to have to remove the $b$. To do this, let's subtract a $b$ from both sides of the equation. This gives us:

$-c = \dfrac{1}{b} - b$

Finally, let's multiply both sides of the equation by -1. This will remove the negative sign before the $c$ term on the left side. This gives us:

$c = b - \dfrac{1}{b}$

Our answer is $\boxed{c = b - \dfrac{1}{b}}$

Answer 2

c=b-1/b

This is the answer