1/y+1 - 2/y-1 + 3/y×y-1
4/3
assuming the usual carelessness with parentheses,
1/(y+1) - 2/(y-1) + 3/(y(y-1))
using a common denominator of y(y+1)(y-1), we have
[y(y-1) - 2y(y+1) + 3(y+1)]/(y(y^2-1))
(3-y^2)/(y(y^2-1))
consistent with her carelessness with brackets, I think
her denominator for the last term was probably y^2 - 1
which makes y^2 - 1 the LCD, and a final answer of
-y/(y^2 - 1) or y/(1 - y^2)
To simplify the expression 1/y+1 - 2/y-1 + 3/y×y-1, we'll follow the order of operations (PEMDAS) and combine like terms.
Step 1: Simplify each fraction separately:
1/y+1 = (1/y) + 1
2/y-1 = (2/y) - 1
3/y×(y-1) = 3/y×y - 3/y×1
Step 2: Simplify each fraction further by finding a common denominator:
For the first fraction (1/y+1 = (1/y) + 1), we need to find the common denominator, which is y.
(1/y) + 1 = (1/y) * (y/y) + 1 * (y/y)
= (y + y) / (y * y)
Simplifying further: 2y / y^2
For the second fraction (2/y-1 = (2/y) - 1), the common denominator is y.
(2/y) - 1 = (2/y) - (1 * y/y)
= (2 - y) / y
For the third fraction (3/y×(y-1) = 3/y×y - 3/y×1), we can simplify both parts separately:
3/y×y = 3y / y^2
3/y×1 = 3/y
Now the expression becomes:
(2y / y^2) - ((2 - y) / y) + (3y / y^2) - (3 / y)
Step 3: Combine like terms:
To combine fractions, we need a common denominator, which is y^2.
(2y / y^2) - ((2 - y) / y) + (3y / y^2) - (3 / y)
= (2y * y / y^2) - ((2 - y) * y^2 / y^2) + (3y * y / y^2) - (3 * y^2 / y^2)
= (2y^2 / y^2) - ((2 - y) * y^2 / y^2) + (3y^2 / y^2) - (3 * y^2 / y^2)
= (2y^2 - y^2 + 3y^2 - 3y^2) / y^2
= (y^2) / y^2
= 1
Therefore, the simplified expression is 1.