Questions: Simplify. [ frac3(3 x^2+16 x+22)(3 x^2+20 x+32) ]

Simplify. [ frac3(3 x^2+16 x+22)(3 x^2+20 x+32) ]
Transcript text: Simplify. \[ \frac{3\left(3 x^{2}+16 x+22\right)}{\left(3 x^{2}+20 x+32\right)} \] Exponent
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Solution

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Solution Steps

To simplify the given expression, we need to factorize both the numerator and the denominator and then cancel out any common factors.

Step 1: Define the Expression

We start with the expression

\[ \frac{3(3x^2 + 16x + 22)}{3x^2 + 20x + 32} \]

Step 2: Expand the Numerator

Expanding the numerator gives us:

\[ 3(3x^2 + 16x + 22) = 9x^2 + 48x + 66 \]

Step 3: Write the Full Expression

Now, we can rewrite the expression as:

\[ \frac{9x^2 + 48x + 66}{3x^2 + 20x + 32} \]

Step 4: Simplify the Expression

The expression can be simplified further, but in this case, it remains as:

\[ \frac{3(3x^2 + 16x + 22)}{3x^2 + 20x + 32} \]

Final Answer

The simplified expression is

\[ \boxed{\frac{3(3x^2 + 16x + 22)}{3x^2 + 20x + 32}} \]

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