Respuesta :
Answer:
[tex]\frac{x^2+5x+6}{x+2}[/tex]
⇒ [tex]x+3[/tex]
Step-by-step explanation:
To simplify:
[tex]\frac{x^2+5x+6}{x+2}[/tex]
To simplify the given expression we need to factor the numerator.
We have
[tex]x^2+5x+6[/tex]
Using split the middle term method by splitting [tex]5x[/tex] into two terms [tex]ax[/tex] and [tex]bx[/tex] such that [tex]ax+bx=5x[/tex] and [tex]ax(bx)=6x^2[/tex]
We see that [[tex]ax=2x[/tex] and [tex]bx=3x[/tex]]
Thus we can write
⇒ [tex]x^2+2x+3x+6[/tex]
Factoring in pairs by taking the GCF of terms in pairs.
⇒ [tex]x(x+2)+3(x+2)[/tex]
Factoring the whole expression as [tex](x+2)[/tex]is a common factor.
⇒ [tex](x+2)(x+3)[/tex]
Now, the expression can be rewritten as:
[tex]\frac{(x+2)(x+3)}{x+2}[/tex]
Canceling out the common expressions, we have.
⇒ [tex]x+3[/tex]
