How do you solve #\frac { x - 1} { x + 3} = \frac { x + 2} { x }#?

1 Answer
mimi
Jun 14, 2017

#x=-1#

Explanation:

Since this is set up like a proportion, cross multiply.
#(x-1)/(x+3) = (x+2)/x#
#(x)(x-1)=(x+2)(x+3)#

Multiply out both sides, respectively.
#(x)(x-1)=(x+2)(x+3)#
#x^2-x=x^2+3x+2x+6#
#x^2-x=x^2+5x+6#

Begin isolating #x# to one side by subtracting both sides by #x^2#.
#x^2-x=x^2+5x+6#
#-x=5x+6#

Subtract both sides by #5x# to get #x# all onto the left side.
#-x=5x+6#
#-6x=6#

Divide by #-6# on both sides to isolate #x#, leaving you with the solution of the equation.
#-6x=6#
#x=-1#

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