Questions: Perform the indicated operation. [ frac9 x^2x^2-36 cdot fracx+63 x ]

Perform the indicated operation. [ frac9 x^2x^2-36 cdot fracx+63 x ]
Transcript text: Perform the indicated operation. \[ \frac{9 x^{2}}{x^{2}-36} \cdot \frac{x+6}{3 x} \]
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Solution

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Solution Steps

Step 1: Factor the Denominator

The first step is to factor the denominator of the first fraction. The expression \(x^2 - 36\) can be factored using the difference of squares formula:

\[ x^2 - 36 = (x - 6)(x + 6) \]

Step 2: Multiply the Fractions

Next, multiply the two fractions:

\[ \frac{9x^2}{(x - 6)(x + 6)} \cdot \frac{x + 6}{3x} \]

Combine the numerators and the denominators:

\[ \frac{9x^2 \cdot (x + 6)}{(x - 6)(x + 6) \cdot 3x} \]

Step 3: Simplify the Expression

Cancel out the common factor \((x + 6)\) from the numerator and the denominator:

\[ \frac{9x^2}{(x - 6) \cdot 3x} \]

Further simplify by canceling out the common factor \(3x\):

\[ \frac{3x}{x - 6} \]

Final Answer

The simplified expression is:

\[ \boxed{\frac{3x}{x - 6}} \]

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