Question

Simplify quantity x squared plus 5 x plus 6 end quantity over quantity x plus 2 x2 + 1 x2 − 1 x + 3 x − 3

Answer 1

Answer X+3

Explanation:

Answer 2

`(x^2+5x+6)/(x+2)`

⇒
`x+3`

Explanation:

To simplify:

`(x^2+5x+6)/(x+2)`

To simplify the given expression we need to factor the numerator.

We have

`x^2+5x+6`

Using split the middle term method by splitting
`5x` into two terms
`ax` and
`bx` such that
`ax+bx=5x` and
`ax(bx)=6x^2`

We see that [
`ax=2x` and
`bx=3x`]

Thus we can write

⇒
`x^2+2x+3x+6`

Factoring in pairs by taking the GCF of terms in pairs.

⇒
`x(x+2)+3(x+2)`

Factoring the whole expression as
`(x+2)`is a common factor.

⇒
`(x+2)(x+3)`

Now, the expression can be rewritten as:

`((x+2)(x+3))/(x+2)`

Canceling out the common expressions, we have.

⇒
`x+3`