How do you solve \frac { 5} { y - 2} = \frac { y } { 3}?

1 Answer
Jan 10, 2018

See a solution process below:

Explanation:

First, multiply each side of the equation by color(red)(3)color(blue)((y - 2)) to eliminate the fractions while keeping the equation balanced:

color(red)(3)color(blue)((y - 2)) xx 5/(y - 2) = color(red)(3)color(blue)((y - 2)) xx y/3

color(red)(3)cancel(color(blue)((y - 2))) xx 5/color(blue)(cancel(color(black)(y - 2))) = cancel(color(red)(3))color(blue)((y - 2)) xx y/color(red)(cancel(color(black)(3)))

color(red)(3) xx 5 = color(blue)((y - 2)) xx y

15 = y^2 - 2y

Next, put the equation in standard form:

15 - color(red)(15) = y^2 - 2y - color(red)(15)

0 = y^2 - 2y - 15

y^2 - 2y - 15 = 0

Then factor the left side of the equation as:

(y - 5)(y + 3) = 0

Now, solve each term on the left for 0:

Solution 1:

y - 5 = 0

y - 5 + color(red)(5) = 0 + color(red)(5)

y - 0 = 5

y = 5

Solution 2:

y + 3 = 0

y + 3 - color(red)(3) = 0 - color(red)(3)

y + 0 = -3

y = -3

The Solutions Are:

y = {-3, 5}