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Airida [17]
2 years ago
7

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

Mathematics
2 answers:
Pavel [41]2 years ago
5 0
<h2>Answer:</h2>

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}
<h2>Step-by-step explanation:</h2>

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}

Genrish500 [490]2 years ago
3 0
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}
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