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How do you simplify #(3x^2-3x-6)/(x^2-4)#?

Answer 1

Nathan Axel

#(3(x+1))/(x+2)#

#"factorise the numerator/denominator and "# #"cancel any common factors"#

#color(magenta)"factor numerator"#

#"take out a "color(blue)"common factor "3#

#rArr3(x^2-x-2)#

#"the factors of - 2 which sum to - 1 are - 2 and + 1"#

#=3(x-2)(x+1)#

#color(magenta)"factor denominator"#

#x^2-4" is a "color(blue)"difference of squares"#

#•color(white)(x)a^2-b^2=(a-b)(a+b)#

#rArrx^2-4=x^2-2^2=(x-2)(x+2)#

#rArr(3x^2-3x-6)/(x^2-4)#

#=(3cancel((x-2))(x+1))/(cancel((x-2))(x+2))#

#=(3(x+1))/(x+2)#

#"with restriction "x!=-2#

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Answer 2

Isaiah Anthony

To simplify the expression (3x^2-3x-6)/(x^2-4), we can factor both the numerator and the denominator. The numerator can be factored as 3(x-2)(x+1), and the denominator can be factored as (x-2)(x+2).

Next, we can cancel out the common factors of (x-2) from both the numerator and the denominator.

After canceling out the common factors, the simplified expression becomes 3(x+1)/(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.