Hello How do I simplify from this (x^2+3x+1)/(x+1) to x+2-(1/x+1)? Picture included Thanks
J Jensi New member Joined Sep 11, 2019 Messages 4 Sep 11, 2019 #1 Hello How do I simplify from this (x^2+3x+1)/(x+1) to x+2-(1/x+1)? Picture included Thanks Attachments A.PNG 1.7 KB · Views: 0 B.PNG 1.4 KB · Views: 0
MarkFL Super Moderator Staff member Joined Nov 24, 2012 Messages 3,021 Sep 11, 2019 #3 [MATH]\frac{x^2+3x+1}{x+1}=\frac{x^2+3x+2-1}{x+1}=\frac{(x+2)(x+1)-1}{x+1}=x+2-\frac{1}{x+1}[/MATH] But yeah, division is more general: [MATH]\begin{array}{c|rr}& 1 & 3 & 1 \\ -1 & & -1 & -2 \\ \hline & 1 & 2 & -1 \end{array}[/MATH] This tells us: [MATH]\frac{x^2+3x+1}{x+1}=x+2-\frac{1}{x+1}[/MATH]
[MATH]\frac{x^2+3x+1}{x+1}=\frac{x^2+3x+2-1}{x+1}=\frac{(x+2)(x+1)-1}{x+1}=x+2-\frac{1}{x+1}[/MATH] But yeah, division is more general: [MATH]\begin{array}{c|rr}& 1 & 3 & 1 \\ -1 & & -1 & -2 \\ \hline & 1 & 2 & -1 \end{array}[/MATH] This tells us: [MATH]\frac{x^2+3x+1}{x+1}=x+2-\frac{1}{x+1}[/MATH]