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

1 Answer
EZ as pi
Jul 12, 2016

x = 5/11x=511

Explanation:

2/3 = 2 - (5x-3)/(x-1)23=2−5x−3x−1

In an equation with fractions, we can get rid of denominators completely by multiplying by the LCM of the denominators. Then the denominators can cancel.

In this case the LCM = color(red)(3(x-1))3(x−1)

(color(red)(3(x-1))xx 2)/3 = color(red)(3(x-1))xx2 - (color(red)(3(x-1))xx(5x-3))/(x-1)3(x−1)×23=3(x−1)×2−3(x−1)×(5x−3)x−1

(cancel3(x-1)xx 2)/cancel3 = 6(x-1) - (3cancel(x-1)xx(5x-3))/cancel(x-1)

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

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

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

11x = 5

x = 5/11

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