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How do you simplify #(x²-7x+6)/ (x²-1) div(2x²-12x)/(x+1)#?

Answer 1

Isaiah Anthony

#1/(2x)#

Start off with a question involving algebraic fractions by factoring wherever possible.

#(x²-7x+6)/ (x²-1) div(2x²-12x)/(x+1) " change " div" to "xx " by reciprocal"#

#((x-6)(x-1))/((x+1)(x-1)) xx ((x+1))/(2x(x-6))#

#(cancel((x-6))cancel((x-1)))/(cancel(x+1)cancel(x-1)) xx (cancel(x+1))/(2xcancel((x-6)))" cancel like factors"#

=#1/(2x)#

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Answer 2

Savannah Anderson

To simplify the expression (x²-7x+6)/(x²-1) ÷ (2x²-12x)/(x+1), we can follow these steps:

Factorize the numerator and denominator of both fractions: (x²-7x+6) = (x-1)(x-6) (x²-1) = (x-1)(x+1) (2x²-12x) = 2x(x-6) (x+1) = (x+1)
Rewrite the expression as multiplication by flipping the second fraction: [(x-1)(x-6)/(x-1)(x+1)] * [(x+1)/(2x(x-6))]
Cancel out the common factors in the numerator and denominator: [(x-1)(x-6)/(x-1)(x+1)] * [(x+1)/(2x(x-6))] = [(x-6)/(x+1)] * [1/(2x)] = (x-6)/(2x(x+1))

Therefore, the simplified expression is (x-6)/(2x(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.