Question

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

Answer 1

`y=+-3`

Explanation:

`"multiply both sides by "y-2`

`cancel(y-2)xx5/cancel(y-2)=(y+2)(y-2)`

`5=y^2-4`

`"add 4 to both sides"`

`9=y^2`

`color(blue)"take the square root of both sides"`

`+-sqrt9=ylarrcolor(blue)"note plus or minus"`

`rArry=+-3`

Answer 2

`y=pm3`

Explanation:

First of all it must be `yne 2`, and we can multiply the whole equation by `y-2` and we get

`5=(y-2)(y+2)` now we use that

`(a-b)(a+b)=a^2-b^2`

so we get

`5=y^2-4`

adding `4`

`9=y^2`

so we get `y=pm 3`