How do you solve #(2x)/(x+3)=(3x)/(x-3)#?

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Answer 1 · 2018-05-07T09:56:25

#x = 0 or x=-15#

# {2x}/{x+3} = {3x}/{x-3}#

#2x(x-3) = 3x(x+3) #

#2x(x-3) - 3x(x+3) = 0#

#x(2x -6 - 3x - 9) = 0#

#x(-x-15) = 0#

#x = 0 or x=-15#

Check:

# {2(0)}/(0+3)=0#

#{3(0)}/(0-3) = 0 quad sqrt#

#{2(-15)}/(-15+3) = {-30}/{-12}=5/2#

#{3(-15)}/(-15-3)=45/18 = 5/2 quad sqrt#