How do you solve #(3x+2)/(2x-1)=(5x+6)/(x+4)#?

1 Answer
Sep 25, 2016

Answer:

#x = 2# or #x = -1#

Explanation:

Multiply both sides of the equation by #(2x-1)(x+4)# to get:

#(3x+2)(x+4) = (5x+6)(2x-1)#

Multiply out both sides to get:

#3x^2+14x+8 = 10x^2+7x-6#

Subtract the left hand side from both sides to get:

#0 = 7x^2-7x-14#

#color(white)(0) = 7(x^2-x-2)#

#color(white)(0) = 7(x-2)(x+1)#

Hence #x=2# or #x=-1#

It remains to check that neither of these values causes a denominator to become #0#. The only values that do are #x = 1/2# and #x = -4# so we're good.