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Decompose (7x-x^2)^-1 in elementary fractions .
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We'll write the given expresison as a fraction, using the negative power property:
(7x-x^2)^-1 = 1/(7x-x^2)
We'll get 2 elementary fractions because we notice 2 factors at denominator.
1/(7x-x^2) = 1/x(7 - x)
The fraction 1/x(7 - x) is the result of algebraic addition of 2 elementary fractions, as it follows:
1/x(7 - x) = A/x + B/(7-x) (1)
We'll multiply by x(7 - x) both sides:
1 = A(7-x) + Bx
We'll remove the brackets:
1 = 7A - Ax + Bx
We'll factorize by x to the right side:
1 = x(B-A) + 7A
Comparing expressions of both sides, we'll get:
B-A = 0
A = B
7A = 1 => A = 1/7
B = 1/7
We'll replace A and B into the expression (1) and we'll get the result of decomposition into elementary fractions:
1/x(7 - x) = 1/7x + 1/(49-7x)
Posted by giorgiana1976 on May 7, 2011 at 6:26 PM (Answer #1)
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