How do you solve #(3x)/(x+9)+1=x/(x+9)# and check for extraneous solutions?

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Answer 1 · 2016-11-23T07:05:40

#x=-3#

#(3x)/(x+9)+1=x/(x+9)#

Subtract #x/(x+9)# from both sides.

#(3x)/(x+9)-x/(x+9)+1=0#

Subtract #1# from both sides.

#(3x)/(x+9)-x/(x+9)=-1#

Combine the two terms on the left.

#(3x-x)/(x+9)=-1#

#(2x)/(x+9)=-1#

Multiply both sides by #(x+9)#.

#2x=-1(x+9)#

#2x=-x-9#

Add #x# to both sides.

#3x=-9#

Divide both sides by #3#.

#x=-3#