Question

Which expressions are equivalent to when x0? Check all that apply.

Answer 1

The correct representation of the expression are:

• 
  `(x+4)/(3)((x)/(6))`

• 
  `((x)/(6))(x+4)/(3)`

• 
  `(x^2+4x)/(18)`

Explanation:

We are given an algebraic expression as:

`(x+4)/(3)`÷
`(6)/(x)`

This expression could also be written as:

`=((x+4)/(3))/((6)/(x))`

We know that any expression of the form:

`((a)/(b))/((c)/(d))` is given by:

`((a)/(b))/((c)/(d))=(a* d)/(b* c)}`

Hence, we get the given expression as:

`=((x+4)/(3))/((6)/(x))=((x+4)* x)/(3* 6)\\\\=(x+4)/(3)* (x)/(6)`

Also, on solving we get:

`=((x+4)/(3))/((6)/(x))=(x^2+4x)/(18)`

Answer 2

we have that


`((x+4))/(3) / (6)/(x) = (x*(x+4))/(3*6) \\ \\ = (( x^(2) +4x))/(18)`

therefore

case a)

`((x+4))/(3) * (x)/(6)`
Is equivalent

case b)

`(6)/(x) * ((x+4))/(3)`
Is not equivalent

case c)

`(x)/(6) * ((x+4))/(3)`
Is equivalent

case d)

`((2 x^(2) +4x))/(6)`
Is not equivalent

case e)

`((2 x^(2) +4x))/(18)`
Is equivalent

Hence

the answer is


`((x+4))/(3) * (x)/(6)`


`(x)/(6) * ((x+4))/(3)`


`((2 x^(2) +4x))/(18)`