Question

(x^3-1)/(9x^3)-(x^2-4)/(12x^2-2)

Answer 1

(x^3-1)/(9x^3)-(x^2-4)/(12x^2-2)= =  

Answer 2

To simplify this expression, we need to find a common denominator for the two fractions. The smallest common denominator for these two fractions is the least common multiple of the denominators, which is (9x^3)(12x^2 - 2). We can rewrite each fraction with this common denominator as follows:

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(x^3-1)/(9x^3) = (x^3-1)*(4x^2-1)/(9x^3)*(4x^2-1) = (4x^5 - 4x^2 - x^3 + 1)/(36x^5 - 9x^3)
(x^2-4)/(12x^2-2) = (x^2-4)*(3x^3+1)/(12x^2-2)*(3x^3+1) = (3x^5 + x^2 - 12x^3 - 4)/(36x^5 - 6x^3)

Now we can combine these fractions by adding the numerators and placing the result over the common denominator:

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(x^3-1)/(9x^3)-(x^2-4)/(12x^2-2) = (4x^5 - 4x^2 - x^3 + 1)/(36x^5 - 9x^3) - (3x^5 + x^2 - 12x^3 - 4)/(36x^5 - 6x^3)
= (4x^5 - 4x^2 - x^3 + 1 - 3x^5 - x^2 + 12x^3 + 4)/(36x^5 - 9x^3)
= (x^5 + 11x^3 - 3x^2 + 5)/(36x^5 - 9x^3)

Therefore, (x^3-1)/(9x^3)-(x^2-4)/(12x^2-2) simplifies to (x^5 + 11x^3 - 3x^2 + 5)/(36x^5 - 9x^3).