Question 1174500
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For a moment, let's completely ignore the limit portion or limit notation.


Let's focus on the expression only. So we'll focus on {{{(x^2-4x)/(x^2-16)}}}


Simplifying the expression leads to:
{{{(x^2-4x)/(x^2-16)}}}


{{{(x(x-4))/(x^2-16)}}}


{{{(x(x-4))/((x-4)(x+4))}}}


{{{(x*highlight((x-4)))/(highlight((x-4))(x+4))}}}


{{{(x*cross((x-4)))/(cross((x-4))(x+4))}}}


{{{x/(x+4)}}}


Such a simplification is necessary because plugging x = 4 into the original expression leads to a division by zero error
Note how x^2-16 = 4^2 - 16 = 16 - 16 = 0 would be in the denominator if x = 4.


But with the simplified expression {{{x/(x+4)}}}, we can plug in x = 4 just fine
Doing so gets us {{{x/(x+4) = 4/(4+4) = 4/8 = 1/2}}}


As x gets closer and closer to x = 4, the value of {{{y = x/(x+4)}}} gets closer and closer to y = 1/2 as we apply the limit. As with all limits, we don't actually arrive at the exact value. We only get closer. 


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Answer: 1/2

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