How do you factor $2/3 = 2 - (5x-3)/(x-1)$ ?

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Answer 1 · 2016-08-15T19:18:18

$11x - 5= 0$ does not factor, but can be solved to give $x = 5/11$

We will need to simplify first. This is not in any recognisable form for factoring.

$2/3 = 2 - (5x-3)/(x-1)" "color(blue)(xx 3(x-1))$

Get rid of the denominators:

$2/cancel3color(blue)(xx cancel3(x-1)) = 2color(blue)(xx 3(x-1)) - (5x-3)/cancel((x-1)) color(blue)(xx 3cancel((x-1))$

$2(x-1) = 6(x-1) - 3(5x-3)$

$2x-2 = 6x-6 -15x+9$

$2x-6x+15x = -6+9+2$

This simplifies to a simple linear equation and does not factorise.

$11x = 5$

How do you factor 2/3 = 2 - (5x-3)/(x-1)2/3 = 2 - (5x-3)/(x-1)?