Question

Simplify the rational expression. X^2+3x+2/x^2+6x+5

A. X+2/X+5
B.3x+2/6x+5
C. X+2/2x+5
D. 3/7

Answer 1

`\large\boxed{A.\ (x+2)/(x+5)}`

Explanation:

`x^2+3x+2=x^2+x+2x+2=x(x+1)+2(x+1)=(x+1)(x+2)\\\\x^2+6x+5=x^2+x+5x+5=x(x+1)+5(x+1)=(x+1)(x+5)\\\\(x^2+3x+2)/(x^2+6x+5)=((x+1)(x+2))/((x+1)(x+5))\qquad\text{cancel}\ (x+1)\\\\=(x+2)/(x+5)`