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

Question

asked Nov 15, 2019 36.8k views

2 Answers

Abuybuy · Answer 1 · 2019-11-17T14:58:59+0000

The correct representation of the expression are:

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)

Alfwatt · Answer 2 · 2019-11-21T17:10:17+0000

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