How do you solve #4/(x+2 )*( x^2-4)/(4x-8)#?

Answer 1

#4/(x+2 )*( x^2-4)/(4x-8) = color(green)(1#

#4/(x+2 )*( x^2-4)/(4x-8) = 4/(x+2) X (x^2-2^2)/(4(x-2))#
We know that #color(blue)(a^2 - b^2 = (a+b)(a-b)#
Hence #x^2 - 2^2 = (x + 2)(x - 2)#

The expression will equal

#cancel(4)/cancel((x+2)) X {cancel((x+2))cancel((x-2))}/(cancel(4)cancel((x-2)))#
# = 1#
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Answer 2

To solve the expression 4/(x+2) * (x^2-4)/(4x-8), we can simplify it by canceling out common factors.

First, let's factor the numerator and denominator of each fraction:

  • The numerator of the first fraction, x^2-4, can be factored as (x+2)(x-2).
  • The denominator of the second fraction, 4x-8, can be factored as 4(x-2).

Now, we can cancel out the common factors:

  • The (x+2) in the numerator of the first fraction cancels out with the (x+2) in the denominator of the second fraction.
  • The (x-2) in the numerator of the second fraction cancels out with the (x-2) in the denominator of the first fraction.

After canceling out the common factors, we are left with: 4/4

This simplifies to: 1

Therefore, the expression 4/(x+2) * (x^2-4)/(4x-8) simplifies to 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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