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Home Q & A Board Science-Related Homework Help Mathematics
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gohar90211 gohar90211
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11 years ago
When simplifying the expression (2/x)+(2/x-1)+(2/x+2) . The denominator is x(x+1)(x–1), what is the numerator?

6x^2 + 9x – 4
6x^2 + 8x + 4
6x^2 + 9x + 4
6x^2 + 4x – 4
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11 years ago
The denominator should be x(x - 1)(x + 2).  There is no 'x + 1' in any of the denominators in the expression, so it cannot be in the LCD (lowest common denominator).   

[2(x - 1)(x + 2) + 2(x)(x + 2) + 2(x)(x - 1)] / x(x - 1)(x + 2)

[2(x^2 + x - 2) + 2(x^2 + 2x) + 2(x^2 - 2x)] / x(x - 1)(x + 2)

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

Now, grouping like terms:

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

(6x^2 + 4x - 4) / x(x - 1)(x + 2)

So, the answer is D. 

Hope this helps!  Smiling Face with Open Mouth
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