Question

Simplify: 7x+21/x^2+5x+6 divided by x+6/x+2

Answer 1

7x+21 x+6
............... ÷ .................
x^2+5x+6 x+2

= 7 (x+3) ÷ x + 6
............... ...................
(x+3)(x+2) x+2

= 7 (x+3) * x + 2
............... ...................
(x+3)(x+2) x + 6

= 7
--------
x + 6

Answer 2

`(7)/((x+6))`

Explanation:

Simplify: 7x+21/x^2+5x+6 divided by x+6/x+2

`(7x+21)/(x^2+5x+6) divide \ by (x+6)/(x+2)`

WE change the division by multiplication then we flip the second fraction

`(7x+21)/(x^2+5x+6) * (x+2)/(x+6)`

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)

`(7(x+3))/((x+3)(x+2)) * (x+2)/(x+6)`

Cancel out x+3 at the top and bottom

Also cancel out x+2

so the given expression becomes

`(7)/((x+6))`