How do you solve #\frac { x } { x - 1} = \frac { 2} { x - 1}#?

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Answer 1 · 2017-04-24T18:33:37

#x=2#

#x/(x-1)=2/(x-1)#

Since we have common denominators we can subtract without changing anything

Move #2/(x-1)# to the other side of the equals sign as a negative

#x/(x-1)-2/(x-1)=0#

This also equals

#(x-2)/(x-1)=0#

Multiply both sides by #(x-1)# to remove the denominator

#cancel(x-1)((x-2)/cancel(x-1))=cancel(0(x-1))#

#x-2=0#

#x=2#

VERIFY YOUR ANSWER

Since #x=2#,

#x/(x-1)=2/(x-1)#

#((2))/((2)-1)=2/((2)-1)#

#2/1=2/1#

#2=2#