Chapter 11.2, Problem 2P

(a)

To determine

Find the product $\frac{3x^2}{x+2}·\frac{(x^2+3x+2)}{x}$

Answer to Problem 2P

  $\frac{3x^2}{x+2}·\frac{(x^2+3x+2)}{x}=3x(x+1)$

Explanation of Solution

Given:

Find the product $\frac{3x^2}{x+2}·\frac{(x^2+3x+2)}{x}$

Concept Used:

Find the factors of numerator and denominator, and then cancel out the common factors from the numerator and denominator.

Calculation:

  $\frac{3x^2}{x+2}·\frac{(x^2+3x+2)}{x}=\frac{3·x·x}{(x+2)}·\frac{(x+1)(x+2)}{x}=3x(x+1)$

Thus, $\frac{3x^2}{x+2}·\frac{(x^2+3x+2)}{x}=3x(x+1)$

(b)

To determine

In problem 2, suppose you multiply the numerators and denominators before you factor. Will you still get the same product? Explain.

Answer to Problem 2P

The product will be same.

Explanation of Solution

Given:

In problem 2, suppose you multiply the numerators and denominators before you factor. Will you still get the same product? Explain.

Concept Used:

Product will always be same if you multiply the numerators and denominators before you factor.

Calculation:

  $\frac{3x^2}{x+2}·\frac{(x^2+3x+2)}{x}=\frac{3x^4+9x^3+6x^2}{x^2+2x}$

Now you divide the numerator by the denominator, will get the result: $3x^2+3x=3x(x+1)$

We can say that the product is always same.

Thus, the product will be same.