Answer: [tex]\bold{\dfrac{3n}{7}+\dfrac{5}{7}=\dfrac{3n+5}{7}}[/tex]
Step-by-step explanation:
When adding (sum) or subtracting (difference) fractions, the denominator needs to be the same.
There are an infinite number of ways to create the numerator to result in 3n + 5 --> just make sure the denominator for each fraction is 7.
Examples of a sum:
[tex]\dfrac{3n}{7}+\dfrac{5}{7}=\dfrac{3n+5}{7}\\\\\\\dfrac{2n+5}{7}+\dfrac{n}{7}=\dfrac{3n+5}{7}\\\\\\\dfrac{2n+3}{7}+\dfrac{n+2}{7}=\dfrac{3n+5}{7}[/tex]
Examples of a difference:
[tex]\dfrac{4n+5}{7}-\dfrac{n}{7}=\dfrac{3n+5}{7}\\\\\\\dfrac{6n+7}{7}-\dfrac{3n+2}{7}=\dfrac{3n+5}{7}\\\\\\\dfrac{5n+6}{7}-\dfrac{2n+1}{7}=\dfrac{3n+5}{7}[/tex]
