Problem 10 - Introductory Algebra for College Students

Question

Multiply as indicated. $$\frac{x^{2}+9 x+18}{x+6} \cdot \frac{1}{x+3}$$

Step-by-Step Solution

Answer

The result of the multiplication of the given expressions is 1.

Step 1: Simplification

Rewrite the given expression and simplify it, if it is possible. In this case, one can simplify the numerator of the first fraction. The expression \(x^{2}+9x+18\) can be factored into \((x+3)(x+6)\). By substitifying it then the new expression becomes \(\frac{(x+3)(x+6)}{x+6}\cdot\frac{1}{x+3}\).

Step 2: Simplify the Expression

The rule of multiplication for fractions allows us to simplify them before multiplying. We can do this by canceling out common variables and constants from the numerator and the denominator. Here, (x+6) can be cancelled from both the numerator and denominator of the first fraction and (x+3) can be cancelled from the numerator of the first fraction and the denominator of the second fraction. Doing this, the expression becomes 1.

Step 3: Conclusion

Since there's nothing more to be simplified, our final answer is 1.