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How do you simplify #(2x^2+6x+4)/(4x^-12x-16)#?

Answer 1

Genesis Allen

I will assume the expression in the question should be

#(2x^2+6x+4)/(4x^2-12x-16) = (x+2)/(2(x-4))#

with exclusion #x != -1#

#(2x^2+6x+4)/(4x^2-12x-16)#

#=(2(x^2+3x+2))/(4(x^2-3x-4))#

#=(2(x+1)(x+2))/(4(x+1)(x-4))#

#=(x+2)/(2(x-4))#

with exclusion #x != -1#

If #x = -1# the original expression becomes #0/0# which is not defined.

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Answer 2

Eva Abramson

To simplify the expression (2x^2+6x+4)/(4x^-12x-16), we can start by factoring the numerator and denominator. The numerator can be factored as 2(x+2)(x+1), and the denominator can be factored as 4(x-2)(x+2).

Next, we can cancel out the common factors in the numerator and denominator. In this case, we can cancel out the (x+2) term.

After canceling out the common factor, the simplified expression becomes 2(x+1)/(4(x-2)).

Finally, we can simplify further by dividing both the numerator and denominator by 2. This gives us the final simplified expression of (x+1)/(2(x-2)).

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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.