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How do you simplify #(8x^2+9)/(4x^2-11)#?

Answer 1

Hazel Anglin

#(8x^2+9)/(4x^2-11)=2+31/(4x^2-11)#

#(8x^2+9)/(4x^2-11)#

#=(8x^2-22+22+9)/(4x^2-11)#

#=(8x^2-22)/(4x^2-11)+(22+9)/(4x^2-11)#

#=(2(4x^2-11))/(4x^2-11)+(31)/(4x^2-11)#

#=2+31/(4x^2-11)#

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Answer 2

Abigail Allen

To simplify the expression (8x^2+9)/(4x^2-11), you can start by factoring both the numerator and the denominator. However, in this case, the expression cannot be factored further. Therefore, the next step is to multiply both the numerator and the denominator by the conjugate of the denominator, which is (4x^2+11). This will help eliminate the denominator's square term. After multiplying, you will have (8x^2+9)(4x^2+11) in the numerator and (4x^2-11)(4x^2+11) in the denominator. Expanding these expressions will give you 32x^4 + 88x^2 + 36x^2 + 99 in the numerator and 16x^4 - 121 in the denominator. Combining like terms, the simplified expression becomes (32x^4 + 124x^2 + 99)/(16x^4 - 121).

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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.