How do you simplify #(4x^2-9)/(2x^2+11x+12)# to lowest terms?

Answer 1

Abigail Allen

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

#4x^2-9=(2x-3)(2x+3)# #2x^2+11x+12= (2x+3)(x+4)#

Therefore,

#(4x^2-9)/(2x^2+11x+12) = ((2x-3)(2x+3))/((2x+3)(x+4))#

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

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Answer 2

Eva Abramson

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

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

=#[(2x-3)(2x+3)]/(2x^2+8x+3x+12)#

=# [(2x-3)(2x+3)]/[2x(x+4)+3(x+4)]#

=# [(2x-3)(2x+3)]/[(x+4)(2x+3]#

=#(2x-3)/(x+4)# , #x!=-4#, #x!=-3/2#

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Answer 3

Ethan Adkins

To simplify (4x^2-9)/(2x^2+11x+12) to lowest terms, you can factor both the numerator and denominator. The numerator can be factored as (2x+3)(2x-3), and the denominator can be factored as (2x+3)(x+4). Cancel out the common factor of (2x+3) from both the numerator and denominator. The simplified expression is (2x-3)/(x+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.