Question

How do you solve `1/3 + 2/(3y) = 1/y^2`?

Answer 1

`y in {1, -3}`

Explanation:

Let's start with the original question:

`1/3+2/(3y)=1/y^2`

Now let's get both fractions on the left side to have a common denominator to make it easier for our calculations. We see that `3y` is our common denominator and so rewrite the equation as so:

`y/(3y)+2/(3y)=1/y^2`

Now let's combine the two fractions to create this:

`(y+2)/(3y)=1/y^2`

Now we can go ahead and use cross multiplication to help simplify the equation, turning it into this:

`y^2(y+2)=3y`

Then we use the distributive property to simplify the left side of the equation:

`y^3+2y^2=3y`

`y = 0 or y^2 + 2y - 3 = 0`

two numbers: the sum is -2, the product is `(-3)(+1)`

you shall not divide by zero.