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How do you simplify # (3x^2 - 3) / (6x - 6) # and what are the restrictions?

Answer 1

Eva Adamson

#(3x^2-3)/(6x-6) = (3(x^2-1))/(6(x-1))#

#=(3(x-1)(x+1))/(3(x-1)*2)#

#=(x+1)/2#

with restriction #x != 1#

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Answer 2

Genesis Allen

To simplify the expression (3x^2 - 3) / (6x - 6), we can factor out a common factor of 3 from both the numerator and denominator, resulting in (3(x^2 - 1)) / (6(x - 1)). Next, we can simplify further by canceling out the common factor of 3, giving us (x^2 - 1) / (2(x - 1)). The restrictions for this expression are that x cannot equal 1, as it would result in division by 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.