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How do you simplify #\frac { a ^ { 2} - 8a } { ( a + 4) ( a - 8) }#?

Answer 1

Eva Adamson

#a/(a+4)#

#(a^2-8a)/((a+4)(a-8))#

Factorize the top part into #a(a-8)#

#(a(a-8))/((a+4)(a-8))#

Now, the #(a-8)# parts cancel out.

#=(acancel((a-8)))/((a+4)cancel((a-8)))#

#=a/(a+4)#

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Answer 2

Julia Adams

To simplify the expression (\frac{a^2 - 8a}{(a + 4)(a - 8)}), you first need to factor the numerator and the denominator, then cancel out any common factors:

Step 1: Factor the numerator: (a^2 - 8a = a(a - 8))

Step 2: Factor the denominator: ((a + 4)(a - 8))

Step 3: Rewrite the expression: (\frac{a(a - 8)}{(a + 4)(a - 8)})

Step 4: Cancel out the common factor ((a - 8)) in the numerator and the denominator:

(\frac{a}{a + 4})

So, the simplified form of the expression is (\frac{a}{a + 4}).

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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.