Question

-Rational expressions and Equations-Simplify each and leave answer in factored form

Answer 1

To Simplify each and leave answer in factored form ​

1)

`(18x^3y)/(4x^4y)`

Cancelling the cmmon terms, we get,

`=(9)/(2x)`

2)

`(30+42n)/(9mn)`

Since the denominator is common to both the terms over addition , we get

`=(30)/(9mn)+(42n)/(9mn)`
`=(10)/(3mn)+_{}(14)/(3m)`

3)

`(2x^2+xy-y^2)/(3x^2+3xy)`

we get,

`=(2x^2+xy+xy-xy-y^2)/(3x^2+3xy)`
`=(2x^2+2xy-xy-y^2)/(3x^2+3xy)`
`=(2x^2+2xy)/(3x^2+3xy)-(xy+y^2)/(3x^2+3xy)`

`=(2(x^2+xy))/(3(x^2+xy))-(xy+y^2)/(3x^2+3xy)`
`=(2)/(3)-(xy+y^2)/(3x^2+3xy)`