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

Question

1773 views around the world

You can reuse this answer
Creative Commons License

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

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

$66x-77=42x-56$

$x=7/8$

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