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

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Answer 1 · 2016-01-30T17:35:45

$z=3$

Start by multiplying both sides by $color(blue)(z-3)$ since each fraction has the same denominator on either side of the equation.

$(z-2)/(z-3)=1/(z-3)$

$(z-2)/(z-3)*color(blue)((z-3))=1/(z-3)*color(blue)((z-3))$

Cancel out the $color(blue)(z-3)$ on both sides.

$(z-2)/color(red)cancelcolor(black)(z-3)*color(red)cancelcolor(blue)((z-3))=1/color(red)cancelcolor(black)(z-3)*color(red)cancelcolor(blue)((z-3))$

Rewrite the equation.

$z-2=1$

Isolate for $z$ .

$z-2$ $color(red)(+2)=1$ $color(red)(+2)$

Solve.

$color(green)(z=3)$

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