Question

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

Answer 1

we have that

$\frac{(x+4)}{3} / \frac{6}{x} = \frac{x*(x+4)}{3*6} \\ \\ = \frac{( x^{2} +4x)}{18}$

therefore

case a) 
$\frac{(x+4)}{3} * \frac{x}{6}$
Is equivalent

case b) 
$\frac{6}{x} * \frac{(x+4)}{3}$
Is not equivalent

case c) 
$\frac{x}{6} * \frac{(x+4)}{3}$
Is  equivalent

case d) 
$\frac{(2 x^{2} +4x)}{6}$
Is not equivalent

case e) 
$\frac{(2 x^{2} +4x)}{18}$
Is equivalent

Hence

the answer is

$\frac{(x+4)}{3} * \frac{x}{6}$

$\frac{x}{6} * \frac{(x+4)}{3}$

$\frac{(2 x^{2} +4x)}{18}$

Answer 2

Answer:

The correct representation of the expression are:

•      $\dfrac{x+4}{3}(\dfrac{x}{6})$

•     $(\dfrac{x}{6})\dfrac{x+4}{3}$

•     $\dfrac{x^2+4x}{18}$

Step-by-step explanation:

We are given an algebraic expression as:

        $\dfrac{x+4}{3}$÷$\dfrac{6}{x}$

This expression could also be written as:

$=\dfrac{\dfrac{x+4}{3}}{\dfrac{6}{x}}$

We know that any expression of the form:

$\dfrac{\dfrac{a}{b}}{\dfrac{c}{d}}$ is given by:

$\dfrac{\dfrac{a}{b}}{\dfrac{c}{d}}=\dfrac{a\times d}{b\times c}}$

Hence, we get the given expression as:

$=\dfrac{\dfrac{x+4}{3}}{\dfrac{6}{x}}=\dfrac{(x+4)\times x}{3\times 6}\\\\=\dfrac{x+4}{3}\times \dfrac{x}{6}$

Also, on solving we get:

$=\dfrac{\dfrac{x+4}{3}}{\dfrac{6}{x}}=\dfrac{x^2+4x}{18}$