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How do you simplify #(2a^2-a-6 )/(2a^2+7a+6)*(a^2-2a-8)/(a^2+a-6)#?

Answer 1

Ethan Adkins

#(a-4)/(a+3)#

#(2a^2-a-6)/(2a^2+7a+6) * (a^2-2a-8)/(a^2+a-6)=#

#=(2a^2-4a+3a-6)/(2a^2+4a+3a+6)*(a^2-4a+2a-8)/(a^2-2a+3a-6)=#

#=(2a(a-2)+3(a-2))/(2a(a+2)+3(a+2))*(a(a-4)+2(a-4))/(a(a-2)+3(a-2))=#

#=((2a+3)(a-2))/((2a+3)(a+2))*((a+2)(a-4))/((a+3)(a-2))=(a-4)/(a+3)#

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Answer 2

Jameson Allen

To simplify the expression (2a^2-a-6)/(2a^2+7a+6)*(a^2-2a-8)/(a^2+a-6), we can factorize the numerator and denominator separately, then cancel out any common factors.

The numerator (2a^2-a-6) can be factored as (2a-3)(a+2), and the denominator (2a^2+7a+6) can be factored as (2a+3)(a+2).

The second fraction in the expression, (a^2-2a-8), can be factored as (a-4)(a+2), and the fourth fraction (a^2+a-6) can be factored as (a+3)(a-2).

Now, we can cancel out the common factors between the numerator and denominator. The (a+2) terms cancel out, as well as the (a-4) and (a-2) terms.

After canceling out the common factors, the simplified expression becomes (2a-3)/(2a+3)*(a+3).

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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.