How do you solve this? (6/xy-2/y^2)/(1/x+4/y)Perform the indicated operation and express your answer in the simplest form.
We can multiply each terms in the right bracket by each of the terms within left bracket.
6/xy (1/x +4/y) - (2/y^2) ( x+4/y)
(6/xy)(1/x) +(6/xy)(4/y) -(2/y^2)(x) -(2/y^2)(4/y)
6/x^2y +24/x^2y -2x/y^2 -8y/y^3.
Similarly we can multiply each of the terms of the left bracket by each of the terms of the right bracket. Since multiplication is commutative, both results will be same.
We have to solve (6/xy-2/y^2)/(1/x+4/y)
making the denominator of all the terms in the numerator the same
=> (6*y/xy^2 - 2x/xy^2)/ (1/x + 4/y)
do the same for the terms in the denominator
=> [(6y - 2x)/xy^2] / (y/xy + 4x/xy)
=> [(6y - 2x)/xy^2] / [(y+4x)/xy]
=> [(6y - 2x)*xy] / xy^2*(y+4x)
cancelling the common terms
=>[(6y - 2x)] / y*(y+4x)
=> (6y-2x) / y*(y+4x)
=> 2(3y - x) / y (y+4x)
The required form is : [2*(3y - x)] / [y*(y+4x)]