Question

Question #f78ff

Answer 1

`(y^2 + 11y + 30)/(y + 5) = y + 6`

Explanation:

Given: `(y^2 + 11y + 30)/(y + 5)`

Can be solved by reducing the numerator (top bracket) to see how it will react with the denominator (bottom bracket).

We have `(y^2 + 11y + 30)` that we know can be factored into two terms containing `y` because the `y` exponent is `2`.

`(y`....... `)` `(y`....... `)`

Looking at the 30, we see it can be factored into `2 xx 15`; or `10 xx 3`; or `5 xx 6`.
The last factors look appealing because they will add up to `11` to match the given middle term.

Now: `(y`....... `5`)``(y`.......`6`)`

And we know both signs here must be positive because we had to `add` `5` to `6` to get the `11`.

Then: `(y + 5`)``(y`+ 6)`

Placing our factors into the original equation:

`[(y + 5)(y + 6)]/ (y+5)`

Gives us good news, because one of the factors cancels out the denominator to leave:

`1(y + 6) = (y + 6)`

`(y^2 + 11y + 30)/(y + 5) = y + 6`