Question

A rational expression simplifies to 3. The denominator of the original expression is given. Which polynomial is the numerator?
$\frac{?}{3x^2+15x+18}$

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

Answer 1

$3=3\cdot1=3\cdot\dfrac{3x^2+15x+18}{3x^2+15x+18}=\dfrac{3\cdot(3x^2+15x+18)}{3x^2+15x+18}=\dfrac{9x^2+45x+54}{3x^2+15x+18}$

Answer A.

Answer 2

Answer:

$\frac{3((3x^2+15x+18)}{3x^2+15x+18}=3$

Therefore, option A is correct.

Step-by-step explanation:

We have been given an expression:

$\frac{?}{3x^2+15x+18}$

The simplified form is 3

That means the given rational function is equal to 3

$3=\frac{?}{3x^2+15x+18}$

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

$\frac{3((3x^2+15x+18)}{3x^2+15x+18}=3$

Therefore, option A is correct.