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}