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:

$\frac{x^2+5x+6}{x+2}$

⇒ $x+3$

Step-by-step explanation:

To simplify:

$\frac{x^2+5x+6}{x+2}$

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:

$\frac{(x+2)(x+3)}{x+2}$  

Canceling out the common expressions, we have.

⇒ $x+3$