How do you simplify #(v^2 + v - 12)/ (v^2 + 6v + 8) div (2v - 6)/( v +2)#?

Answer 1

#1/2#

the trynomial

#v^2+(v_1+v_2)v+(v_1*v_2)v#

is obtained by the product:

#(v+v_1)(v+v_2)#

so

#v^2+v-12=(v+4)(v-3)#

and

#v^2+6v+8=(v+4)(v+2)#

So you can rewrite

#(v^2+v-12)/(v^2+6v+8)-:(2v-6)/(v+2)=(cancel((v+4))(v-3))/(cancel((v+4))(v+2))-:(2(v-3))/(v+2)#
#=cancel(v-3)/cancel(v+2)*cancel(v+2)/(2cancel((v-3)))=1/2#
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Answer 2

To simplify the expression, we can start by factoring the numerator and denominator separately.

The numerator, v^2 + v - 12, can be factored as (v + 4)(v - 3).

The denominator, v^2 + 6v + 8, can be factored as (v + 2)(v + 4).

Next, we can rewrite the expression as [(v + 4)(v - 3)] / [(v + 2)(v + 4)] divided by (2v - 6) / (v + 2).

Now, we can simplify further by canceling out common factors.

Canceling out (v + 4) in the numerator and denominator, and (v + 2) in the numerator and denominator, we get (v - 3) / (v + 2) divided by (2v - 6) / 1.

Simplifying the expression, we have (v - 3) / (v + 2) divided by (2v - 6).

To divide by a fraction, we can multiply by its reciprocal.

Therefore, the simplified expression is (v - 3) / (v + 2) multiplied by 1 / (2v - 6).

This can be further simplified as (v - 3) / [(v + 2)(2v - 6)].

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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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