How do you simplify and restricted value of #(x^2-36)/(3x+6) #?

Answer 1

#((x-6)(x+6))/(3(x+2))#; #x != -2#

Given: #(x^2 - 36)/(3x+6)#
The numerator is the difference of squares #(a^2 - b^2) = (a - b)(a + b): (x^2 - 6^2) = (x -6)(x+6)#
Rewriting the given expression yields: #((x -6)(x+6))/(3x + 6)#
The denominator can be factored using the greatest common factor (GCF) of #3: 3(x + 2)#
Rewriting the given expression yields: #((x-6)(x+6))/(3(x+2))#
Since there is a fraction, the denominator cannot be #= 0#. This means that #3(x + 2) != 0#, or #x + 2 != 0#. This occurs when #x = -2#.
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Answer 2

To simplify the expression (x^2-36)/(3x+6), we can factor the numerator and denominator. The numerator is a difference of squares, so it can be factored as (x+6)(x-6). The denominator can be factored out the greatest common factor, which is 3, resulting in 3(x+2).

Therefore, the expression simplifies to (x+6)(x-6)/(3)(x+2).

To find the restricted values, we need to identify any values of x that would make the denominator equal to zero. In this case, the restricted value is x = -2, as it would make the denominator (3)(-2+2) equal to zero.

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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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