Answer:
[tex]\frac{7}{(x+6)}[/tex]
Step-by-step explanation:
Simplify: 7x+21/x^2+5x+6 divided by x+6/x+2
[tex]\frac{7x+21}{x^2+5x+6} divide \ by \frac{x+6}{x+2}[/tex]
WE change the division by multiplication then we flip the second fraction
[tex]\frac{7x+21}{x^2+5x+6} * \frac{x+2}{x+6}[/tex]
Now we factor the expression x^2 + 5x+6
x^2 + 5x +6 becomes (x+3)(x+2)
now factor 7x +21 , it becomes 7(x+3)
[tex]\frac{7(x+3)}{(x+3)(x+2)} * \frac{x+2}{x+6}[/tex]
Cancel out x+3 at the top and bottom
Also cancel out x+2
so the given expression becomes
[tex]\frac{7}{(x+6)}[/tex]
