How do you solve #(2x) / (x-2) = 1 /( 3x-4) + 2=14/11#?

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Answer 1 · 2018-07-09T09:26:08

#x=-7/2, 7/8, 14/11, #

Given that

#\frac{2x}{x-2}=\frac{1}{3x-4}+2=14/11#

#\frac{2x}{x-2}=\frac{6x-7}{3x-4}=14/11#

Taking first & second equality

1.) #\frac{2x}{x-2}=\frac{6x-7}{3x-4} \ \quad \forall \ x\ne 2, x\ne 4/3#

#6x^2-8x=6x^2-19x+14#

#x=14/11#

2) Taking first & third equality

#\frac{2x}{x-2}=14/11\ \quad \forall \ x\ne 2#

#11x=7x-14#

#x=-7/2#

3) Taking second & third equality

#\frac{6x-7}{3x-4}=14/11\ \quad \forall \ x\ne 4/3#

#66x-77=42x-56#

#x=7/8#