Simplify
[(1-3y)/y]/(9/y^2)-1
To simplify the given expression:
Step 1: Simplify the numerator of the main fraction.
In the numerator, distribute the negative sign to each term inside the parentheses:
1 - 3y
Step 2: Simplify the denominator of the main fraction.
In the denominator, simplify the expression:
9/y^2 - 1
To calculate the expression, find a common denominator for the two terms in the denominator:
Since the first term has a denominator of y^2 and the second term has a denominator of 1, we can rewrite the second term with a denominator of y^2:
9/y^2 - 1 * y^2/y^2
Simplifying the denominator:
9/y^2 - y^2/y^2
Next, combine the terms in the denominator:
(9 - y^2)/y^2
Step 3: Simplify the entire fraction.
Now that we have the simplified form of the numerator and denominator, simplify the entire fraction by taking the numerator and dividing it by the denominator:
[(1 - 3y)/y] / (9 - y^2)/y^2
To divide fractions, multiply the first fraction by the reciprocal of the second fraction:
[(1 - 3y)/y] * (y^2/(9 - y^2))
Step 4: Simplify the expression further if possible.
Now, multiply the numerator and denominator of the fraction:
(1 - 3y)(y^2) / y(9 - y^2)
Expand the numerator:
(y^2 - 3y^3) / y(9 - y^2)
Since there is no common factor between the numerator and the denominator, this expression is already in its simplified form.
Therefore, the simplified form of the expression is:
(y^2 - 3y^3) / y(9 - y^2)