How do you multiply #\frac { b ^ { 2} - b - 2} { b + 4} \cdot \frac { b + 4} { b ^ { 2} - 9b + 14}#?

Answer 1

Anna Allen

Factorize denominator and numerator............

#(b^2-b-2)/cancel(b+4)xxcancel(b+4)/(b^2-9b+14)=(b^2-b-2)/(b^2-9b+14)#

#=[(b+1)cancel((b-2))]/[(b-7)cancel((b-2))]=(b+1)/(b-7)#

Anyway, don't trust my arithmetic............

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Answer 2

Caleb Alexander

To multiply $\frac{b^2 - b - 2}{b + 4} \cdot \frac{b + 4}{b^2 - 9b + 14}$ , you should follow these steps:

Factorize each polynomial if possible.
Simplify the expression by canceling out common factors.

Starting with the given expression:

\frac{b^2 - b - 2}{b + 4} \cdot \frac{b + 4}{b^2 - 9b + 14}

First, factorize the polynomials in the numerators and denominators:

The polynomial $b^2 - b - 2$ can be factored into $(b - 2)(b + 1)$ .
The polynomial $b^2 - 9b + 14$ can be factored into $(b - 7)(b - 2)$ .

Substitute these factorizations back into the original expression:

\frac{(b - 2)(b + 1)}{b + 4} \cdot \frac{b + 4}{(b - 7)(b - 2)}

Next, simplify the expression by canceling out common factors. The factors $b + 4$ and $b - 2$ appear in both a numerator and a denominator, so they can be canceled out:

\frac{b + 1}{b - 7}

Thus, the simplified form of the given expression is:

\frac{b + 1}{b - 7}

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.