Equivalent expressions are expressions of equal value.
The equivalent expressions of [tex]\mathbf{(\frac{r}{s})(6)} }[/tex] are [tex]\mathbf{\frac{3(6) - 1}{2(6) + 1}}[/tex] and [tex]\mathbf{ \frac{17}{13}}[/tex]
The expressions are given as:
[tex]\mathbf{r(x) = 3x - 1}[/tex]
[tex]\mathbf{s(x) = 2x + 1}[/tex]
[tex]\mathbf{(\frac{r}{s})(6)}[/tex] is calculated as follows:
We have:
[tex]\mathbf{(\frac{r}{s})(x) = \frac{r(x)}{s(x)}}[/tex]
Substitute expressions for r(x) and g(x)
[tex]\mathbf{(\frac{r}{s})(x) = \frac{3x - 1}{2x + 1}}[/tex]
Substitute 6 for x
[tex]\mathbf{(\frac{r}{s})(6) = \frac{3(6) - 1}{2(6) + 1}}[/tex]
Expand
[tex]\mathbf{(\frac{r}{s})(6) = \frac{18- 1}{12 + 1}}[/tex]
[tex]\mathbf{(\frac{r}{s})(6) = \frac{17}{13}}[/tex]
Hence, the equivalent expressions of [tex]\mathbf{(\frac{r}{s})(6)} }[/tex] are [tex]\mathbf{\frac{3(6) - 1}{2(6) + 1}}[/tex] and [tex]\mathbf{ \frac{17}{13}}[/tex]
Read more about equivalent expressions at:
https://brainly.com/question/2737200
