How do you solve $\frac{2}{3} = 2 - \frac{5 x - 3}{x - 1}$ $2/3 = 2 - (5x-3)/(x-1)$ ?

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Answer 1 · 2017-07-13T14:49:40

$x = \frac{5}{11} =$ $color(magenta)(x=5/11=$ extraneous solution

$\frac{2}{3} = 2 - \frac{5 x - 3}{x - 1}$ $2/3=2-(5x-3)/(x-1)$

$:.-(5x-3)/(x-1)=2/3-2$

multiply both sides by $-1$

$:.(5x-3)/(x-1)=-2/3+2$

multiply both sides by $x-1$

$:.5x-3=-2/3(x-1)+2(x-1)$

$:.5x-3=-2/3x+2/3+2x-2$

$:.5x+2/3x-2x=2/3-2+3$

$:.3 2/3x=3 2/3-2$

$:.11/3x=3 2/3-2$

$:.11/3x=1 2/3$

$:.11/3x=5/3$

$:.x=(5/3)/(11/3)$

$:.x=5/cancel3^1 xx cancel3^1/11$

$:.color(magenta)(x=5/11=$ extraneous solution

How do you solve 2/3 = 2 - (5x-3)/(x-1)23=2−5x−3x−12/3 = 2 - (5x-3)/(x-1)?