Question

How do you simplify `(8a^2-6a-9)/( 6a^2-5a-6) ÷ (4a^2+11a+6)/( 9a^2+12a+4)`?

Answer 1

`(3a+2)/(a+2)`

Explanation:

`{(8a^2-6a-9)/(6a^2-5a-6)}-: {(4a^2+11a+6)/(9a^2+12a+4)}`

`={(8a^2-12a+6a-9)/(6a^2-9a+4a-6)}-: {(4a^2+8a+3a+6)/(9a^2+6a+6a+4)}`

`={(4a(2a-3)+3(2a-3))/(3a(2a-3)+2(2a-3))}-: {(4a(a+2)+3(a+2))/(3a(3a+2)+2(3a+2))}`

`={(cancel((2a-3))(4a+3))/(cancel((2a-3))(3a+2))}-: {((a+2)(4a+3))/((3a+2)(3a+2))}`

`=cancel((4a+3))/cancel((3a+2))*(cancel((3a+2))(3a+2))/((a+2)cancel((4a+3)))`

`(3a+2)/(a+2)` [Ans]