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How do you simplify #(x^2 - 7x + 6)/(x^2-36)#?

Answer 1

Eli Assouline

#(x^2-7x+6)/(x^2-36)=color(green)((x-1)/(x+6)#
(assuming #x!=+-6# so the original expression is valid).

Factoring #color(white)("XXX")x^2-7x+6 = (x-6)(x-1)#

#color(white)("XXX")x^2-36=(x-6)(x+6)#

So #color(white)("XXX")(x^2-7x+6)/(x^2-36)=(cancel(""(x-6))(x-1))/(cancel(""(x-6))(x+6)#

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Answer 2

Eva Adamson

To simplify the expression (x^2 - 7x + 6)/(x^2-36), we can factor both the numerator and the denominator. The numerator can be factored as (x - 6)(x - 1), and the denominator can be factored as (x - 6)(x + 6).

Next, we can cancel out the common factor of (x - 6) in both the numerator and the denominator.

Therefore, the simplified form of (x^2 - 7x + 6)/(x^2-36) is (x - 1)/(x + 6).

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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.