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Write as a sum of fractions 1/y(y+1)
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We have to express 1 / y(y+1) as the sum of two fractions.
Let us write 1 / y(y+1) as A / y + B / (y + 1)
=> [A( y + 1) + By]/ y(y+1) = 1 / y(y+1)
=> Ay + A + By = 1
=> y ( A + B) + A = 1
Now equate the terms with y and the numeric terms.
=> A + B = 0 and A = 1
=> A = 1 and B = -A = -1
Therefore we can write 1 / y(y+1) as 1/y - 1/(y+1)
Posted by justaguide on December 4, 2010 at 1:54 AM (Answer #1)
We remark that the denominator of the given ratio is the least common denominator of 2 irreducible ratios.
The final ratio 1/y(y+1) is the result of addition or subtraction of 2 elementary fractions, as it follows:
1/y(y+1) = A/y + B/(y+1) (1)
We'll multiply by y(y+1) both sides:
1 = A(y+1) + By
We'll remove the brackets:
1 = Ay + A + By
We'll factorize by y to the right side:
1 = y(A+B) + A
We'll compare expressions of both sides:
A+B = 0
A = 1
1 + B = 0
B = -1
We'll substitute A and B into the expression (1) and we'll get the algebraic sum of 2 elementary fractions:
1/y(y+1) = 1/y - 1/(y+1)
Posted by giorgiana1976 on December 4, 2010 at 1:53 AM (Answer #2)
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