How do you simplify #(12x^2+6x+90)/(6x^2-54)#?

Answer 1

#=((2x^2 +x +15))/((x+3)(x-3)#

With algebraic fractions, always try to find factors first..

#(6(2x^2 +x +15))/(6(x^2 -9))" "larr# common factor of 6
#=(6(2x^2 +x +15))/(6(x+3)(x-3)#
#=((2x^2 +x +15))/((x+3)(x-3)#

This does not simplify further.

However, if the numerator had been #12x^2+6x-90#

We would have:

#(6(2x^2 +x -15))/(6(x^2 -9)#
#=(6(2x-5)(x+3))/(6(x+3)(x-3))#
#= ((2x+5))/((x-3))#
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Answer 2

To simplify the expression (12x^2+6x+90)/(6x^2-54), we can start by factoring the numerator and the denominator. The numerator can be factored as 6(2x^2+x+15), and the denominator can be factored as 6(x^2-9).

Next, we can cancel out the common factor of 6, leaving us with (2x^2+x+15)/(x^2-9).

Now, we can further simplify by factoring the numerator and the denominator. The numerator cannot be factored any further, but the denominator can be factored as (x+3)(x-3).

Therefore, the simplified expression is (2x^2+x+15)/((x+3)(x-3)).

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Answer 3

To simplify the expression (12x^2 + 6x + 90) / (6x^2 - 54), you can start by factoring both the numerator and denominator, and then simplifying the fraction by canceling out common factors.

Factor the numerator: 12x^2 + 6x + 90 = 6(2x^2 + x + 15)

Factor the denominator: 6x^2 - 54 = 6(x^2 - 9) = 6(x + 3)(x - 3)

Now, rewrite the expression: (6(2x^2 + x + 15)) / (6(x + 3)(x - 3))

Cancel out the common factor of 6: (2x^2 + x + 15) / (x + 3)(x - 3)

Therefore, the simplified form of the expression is: (2x^2 + x + 15) / (x + 3)(x - 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.

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.

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.

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.

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