Question

A rational expression simplifies to 3. The denominator of the original expression is given. Which polynomial is the numerator?


`(?)/(3x^2+15x+18)`

A.
`9x^2+45x+54`
B.
`x^2+5x+6`
C.
`3x^2+15x+54`
D.
`3x+6`

Answer 1

`(3((3x^2+15x+18))/(3x^2+15x+18)=3`

Therefore, option A is correct.

Explanation:

We have been given an expression:

`(?)/(3x^2+15x+18)`

The simplified form is 3

That means the given rational function is equal to 3

`3=(?)/(3x^2+15x+18)`

Now, we will choose the first option

`9x^2+45x+54`

Taking 3 common from above equation we get:

`3(3x^2+15x+18)`

Hence, when we put the above equation in numerator denominator and numerator gets cancel and final result will be 3

`(3((3x^2+15x+18))/(3x^2+15x+18)=3`

Therefore, option A is correct.

Answer 2

`3=3\cdot1=3\cdot(3x^2+15x+18)/(3x^2+15x+18)=(3\cdot(3x^2+15x+18))/(3x^2+15x+18)=(9x^2+45x+54)/(3x^2+15x+18)`

Answer A.