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.

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neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

(6/xy -2/y^2)(1/x+4/y)

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. 

william1941's profile pic

william1941 | College Teacher | (Level 3) Valedictorian

Posted on

We have to solve (6/xy-2/y^2)/(1/x+4/y)

Now (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)]

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