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

Accepted Solution

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]