How do you simplify #4/(x-2)-3/(x+1)+2/(x^2-x-2)#?

Answer 1

#(x+12)/((x-2)(x+1))=(x+12)/(x^2-x-2)#

#4/(x-2)-3/(x+1)+2/(x^2-x-2)#

We need the denominators to be the same. We can do that by multiplying through with various forms of the number 1:

#4/(x-2)(1)-3/(x+1)(1)+2/((x-2)(x+1))#
#4/(x-2)((x+1)/(x+1))-3/(x+1)((x-2)/(x-2))+2/((x-2)(x+1))#
#(4(x+1))/((x-2)(x+1))-(3(x-2))/((x+1)(x-2))+2/((x-2)(x+1))#
#(4x+4)/((x-2)(x+1))-(3x-6)/((x+1)(x-2))+2/((x-2)(x+1))#
#((4x+4)-(3x-6)+2)/((x-2)(x+1))#
#(4x+4-3x+6+2)/((x-2)(x+1))#
#(x+12)/((x-2)(x+1))=(x+12)/(x^2-x-2)#
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Answer 2

To simplify the expression 4/(x-2) - 3/(x+1) + 2/(x^2-x-2), we need to find a common denominator for all the fractions. The common denominator is (x-2)(x+1).

Multiplying the first fraction by (x+1)/(x+1), the second fraction by (x-2)/(x-2), and the third fraction by (x-2)(x+1)/(x-2)(x+1), we get:

(4(x+1))/((x-2)(x+1)) - (3(x-2))/((x-2)(x+1)) + (2(x-2)(x+1))/((x-2)(x+1))

Simplifying further, we have:

(4x + 4 - 3x + 6 + 2x^2 - 2x - 4)/(x^2 - 3x - 2)

Combining like terms, we get:

(2x^2 - 3x + 6)/(x^2 - 3x - 2)

This is the simplified form of the expression 4/(x-2) - 3/(x+1) + 2/(x^2-x-2).

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Answer 3

To simplify the expression ( \frac{4}{x-2} - \frac{3}{x+1} + \frac{2}{x^2 - x - 2} ), first, find a common denominator for all the fractions. Then, combine them into a single fraction.

The common denominator for the three fractions is ( (x-2)(x+1)(x-2) ).

Rewriting each fraction with the common denominator:

[ \frac{4(x+1)}{(x-2)(x+1)} - \frac{3(x-2)}{(x-2)(x+1)} + \frac{2}{(x-2)(x+1)} ]

Combining the fractions:

[ \frac{4(x+1) - 3(x-2) + 2}{(x-2)(x+1)} ]

[ \frac{4x + 4 - 3x + 6 + 2}{(x-2)(x+1)} ]

[ \frac{x + 12}{(x-2)(x+1)} ]

So, the simplified expression is ( \frac{x + 12}{(x-2)(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.

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.

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.

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.

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