Question

(3xy/3x^2-12)*(x^2+3x+2/xy+y)

Answer 1

Value of expression
`(3xy/3x^2-12)*(x^2+3x+2/xy+y)` is
`(x)/(x-2)` .

Explanation:

Here we need to evaluate expression : (3xy/3x^2-12)*(x^2+3x+2/xy+y) or ,

`(3xy/3x^2-12)*(x^2+3x+2/xy+y)`

Let's simplify this

⇒
`((3xy)/(3x^2-12))((x^2+3x+2)/(xy+y))`

Factorizing the terms we get:

⇒
`((3xy)/(3(x^2-4)))((x^2+2x+x+2)/(y(x+1)))` {
`a^2-b^2=(a+b)(a-b)` }

⇒
`((xy)/((x-2)(x+2)))((x(x+2)+1(x+2))/(y(x+1)))`

⇒
`((xy)/((x-2)(x+2)))(((x+1)(x+2))/(y(x+1)))`

Cancelling similar terms we get:

⇒
`(x)/(x-2)`

Therefore , Value of expression
`(3xy/3x^2-12)*(x^2+3x+2/xy+y)` is
`(x)/(x-2)` .