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)#