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How do you simplify #(x^2-3x+2)/(x^2+5x-6)#?

Answer 1

Kennedy Adams

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

The first step is to factorise both numerator and denominator.

Both are quadratics and can be factorised using the a-c method.

#rArrx^2-3x+2=(x-2)(x-1)#

and #x^2+5x-6=(x+6)(x-1)#

#rArr(x^2-3x+2)/(x^2+5x-6)=((x-2)(cancel(x-1)))/((x+6)(cancel(x-1)))=(x-2)/(x+6)#

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Answer 2

Kennedy Adams

To simplify the expression (x^2-3x+2)/(x^2+5x-6), you can factor both the numerator and the denominator. The numerator factors to (x-1)(x-2), and the denominator factors to (x+6)(x-1). Cancel out the common factor of (x-1) from both the numerator and the denominator. The simplified expression is (x-2)/(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.