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How do you simplify and find the restrictions for #(x-1)/( (x-3)(x+1))#?

Answer 1

Isaiah Anthony

#x!=3,-1#

#"the rational function is already in simplest form"#

#"the restrictions are any values of x that would make the"# #"rational function undefined"#

#"equating the denominator to zero and solving gives the"# #"values that x cannot be"#

#"solve "(x-3)(x+1)=0#

#rArrx=3,x=-1larrcolor(red)"are restricted values"#

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Answer 2

Isaiah Anthony

To simplify the expression (x-1)/((x-3)(x+1)), we can start by factoring the denominator.

The denominator (x-3)(x+1) is a product of two binomials.

Next, we can look for any common factors between the numerator (x-1) and the denominator. In this case, there are no common factors.

To find the restrictions, we need to identify any values of x that would make the denominator equal to zero.

Setting each factor equal to zero, we find that x = 3 and x = -1 would make the denominator zero.

Therefore, the restrictions for the expression are x ≠ 3 and x ≠ -1.

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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.