How do you solve ((z-2)/(z-3)) = (1/(z-3))?

Jan 30, 2016

$z = 3$

Explanation:

Start by multiplying both sides by $\textcolor{b l u e}{z - 3}$ since each fraction has the same denominator on either side of the equation.

$\frac{z - 2}{z - 3} = \frac{1}{z - 3}$

$\frac{z - 2}{z - 3} \cdot \textcolor{b l u e}{\left(z - 3\right)} = \frac{1}{z - 3} \cdot \textcolor{b l u e}{\left(z - 3\right)}$

Cancel out the $\textcolor{b l u e}{z - 3}$ on both sides.

$\frac{z - 2}{\textcolor{red}{\cancel{\textcolor{b l a c k}{z - 3}}}} \cdot \textcolor{red}{\cancel{\textcolor{b l u e}{\left(z - 3\right)}}} = \frac{1}{\textcolor{red}{\cancel{\textcolor{b l a c k}{z - 3}}}} \cdot \textcolor{red}{\cancel{\textcolor{b l u e}{\left(z - 3\right)}}}$

Rewrite the equation.

$z - 2 = 1$

Isolate for $z$.

$z - 2$ $\textcolor{red}{+ 2} = 1$ $\textcolor{red}{+ 2}$

Solve.

$\textcolor{g r e e n}{z = 3}$