How do you simplify #(7x+14)/(7x^2-7x-42)#?

Answer 1

#color(blue)(1/(x-3))#

#(7x+14)/(7x^2-7x-42)#

Take 7 out of the denominator and numerator:

#(7(x+2))/(7(x^2-x-6))#

Cancel:

#(cancel(7)(x+2))/(cancel(7)(x^2-x-6))=((x+2))/((x^2-x-6))#

Denominator of a factor:

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

Cancel:

#(cancel((x+2)))/(cancel((x+2))(x-3))=color(blue)(1/(x-3))#

It is also possible to get this result by factoring the denominator initially, although this is a little trickier to do than factoring in stages:

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Answer 2

To simplify the expression (7x+14)/(7x^2-7x-42), we can first factor the numerator and denominator. The numerator can be factored as 7(x+2), while the denominator can be factored as 7(x-6)(x+1).

Next, we can cancel out the common factors of 7, resulting in (x+2)/(x-6)(x+1).

Therefore, the simplified form of (7x+14)/(7x^2-7x-42) is (x+2)/(x-6)(x+1).

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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.

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.

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.

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.

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