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Example 1
$\dfrac{1}{3+\dfrac{1}{x+3}}=$
- $\dfrac{3x+10}{x+3}$
- $3+\dfrac{1}{x+3}$
- $\dfrac{x+3}{3x+10}$
- $\dfrac{x+3}{3}$
- $\dfrac{1}{x+6}$
Solution
This example is about simplifying rational expressions.
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The 5 possible answers are simple rational expressions and therefore we need to rewrite the given expression as a simple rational expression in order to be able to compare it to the 5 answers. Let us add the two terms in the denominator $3+\dfrac{1}{x+3}$ as follows
$3+\dfrac{1}{x+3}=\dfrac{3(x+3)}{x+3}+\dfrac{1}{x+3}=\dfrac{3x+10}{x+3}$
The given expression is equivalent to
$\dfrac{1}{\dfrac{3x+10}{x+3}}$
Rewrite $1$ in the numerator as a fraction
$= \dfrac{\dfrac{1}{1}}{\dfrac{3x+10}{x+3}}$
To divide two rational expressions, we multiply the first by the reciprocal of the second. Hence
$=\dfrac{1}{1} \times \dfrac{x+3}{3x+10}$
$=\dfrac{x+3}{3x+10}$
Answer C
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