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How do you simplify #(4c^2+12c+9)/(2c^2-11c-21)#?

Answer 1

Eva Abramson

Factoring the numerator and denominator and then cancelling common terms gives:
#color(white)("XXXX")##(2c+3)/(c-7)#

#(4c^2+12c+9)/(2c^2-11c-21)#

#color(white)("XXXX")##= ((2c+3)(2c+3))/((2c+3)(c-7))#

#color(white)("XXXX")##= (2c+3)/(c-7)#

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Answer 2

Abigail Allen

To simplify the expression (4c^2+12c+9)/(2c^2-11c-21), you can factor both the numerator and the denominator. The numerator can be factored as (2c+3)^2, and the denominator can be factored as (2c+3)(c-7).

By canceling out the common factor of (2c+3), the simplified expression becomes (2c+3)/(c-7).

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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.