Questions: (x^2+14x+45)/(x^2+4x-32) * (x^2+2x-24)/(x^2+18x+81)=

Transcript text: \[ \frac{x^{2}+14 x+45}{x^{2}+4 x-32} \cdot \frac{x^{2}+2 x-24}{x^{2}+18 x+81}= \]

Solution

Solution Approach

Factor each quadratic expression in the numerators and denominators.
Cancel out any common factors between the numerators and denominators.
Multiply the remaining factors in the numerators and denominators to get the simplified product.

Step 1: Factor the Expressions

We start by factoring the given quadratic expressions:

Step 2: Set Up the Product

We can now express the product of the fractions as follows:

\[ \frac{(x + 5)(x + 9)}{(x - 4)(x + 8)} \cdot \frac{(x - 4)(x + 6)}{(x + 9)^2} \]

Step 3: Cancel Common Factors

Next, we cancel the common factors in the numerator and denominator:

After canceling, we have:

\[ \frac{(x + 5)(x + 6)}{(x + 8)(x + 9)} \]

Thus, the simplified product is:

\[ \boxed{\frac{(x + 5)(x + 6)}{(x + 8)(x + 9)}} \]

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