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How do you divide # (x^2-5x-14)/(x-7)div(x+2)/(x^2-9)#?

Answer 1

Savannah Anderson

Dividing is the same as multiplying by the reciprocal.

So #(x^2-5x-14)/(x-7) div (x+2)/(x^2-9)# is the same as #(x^2-5x-14)/(x-7) xx (x^2-9)/(x+2)#

We can simplify this by factoring

#((x-7)(x+2))/(x-7)xx(x^2-9)/(x+2)#

#(cancel(color(red)((x-7)))cancel(color(blue)((x+2))))/cancel(color(red)((x-7)))xx(x^2-9)/cancel(color(blue)((x+2))#

#= x^2-9#

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Answer 2

Eli Assouline

To divide the expression (x^2-5x-14)/(x-7) by (x+2)/(x^2-9), we can simplify the expression by factoring and canceling out common factors.

First, let's factor the numerator and denominator separately:

Numerator (x^2-5x-14): (x^2-5x-14) can be factored as (x-7)(x+2).

Denominator (x-7): The denominator (x-7) cannot be factored further.

Next, let's factor the denominator (x+2)/(x^2-9): (x^2-9) can be factored as (x-3)(x+3).

Now, we can rewrite the expression and cancel out common factors:

[(x-7)(x+2)] / [(x-7)(x-3)(x+3)]

By canceling out the common factor (x-7), the expression simplifies to:

(x+2) / (x-3)(x+3)

Therefore, the simplified expression is (x+2) / (x-3)(x+3).

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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.