Question

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

Answer 1

`x = 5/11`

Explanation:

`2/3 = 2 - (5x-3)/(x-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))`

`(color(red)(3(x-1))xx 2)/3 = color(red)(3(x-1))xx2 - (color(red)(3(x-1))xx(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`