Question

How do you solve `5/(y-2)=y+2`?

Answer 1

`y = +-3`

Explanation:

`5/(y-2) = y+2`

First of all, we multiply both sides by `y-2`:
`5 = (y+2)(y-2)`

`5 = y^2 - 4`

`9 = y^2`

`y = +-3`

Now we have to check both of our solutions back into the original equation to make sure both are really solutions:
`5/(-3-2)=-3+2`

`5/-5 = -1`

`-1 = -1`

Now we know that `-3` works. Now let's check `3`:
`5/(3-2) = 3+2`

`5/1 = 5`

`5 = 5`

Good. Both solutions work. So the answer is `y = +-3`.

Hope this helps!

Answer 2

`y = +-3`

Explanation:

`5/(y - 2) = y + 2`

Multiply `(y - 2)` on both the sides

`5/cancel((y - 2)) × cancel((y -2)) = (y + 2) × (y -2)`

`5 = (y + 2) × (y - 2)`

`5 = y^2 - 2^2 color(white)(..)[∵ (a + b)(a - b) = a^2 - b^2)`

`5 = y^2 - 4`

Add `4` on both the sides

`5 + 4 = y^2 - 4 + 4`

`9 = y^2`

Square root on both the sides

`sqrt(9) =sqrt(y^(2))`

`color(blue)(y = +-3)`