PLEASE ANSWER!!!! WILL GIVE 20 POINTS!!!! The sum of the numerator and the denominator of the certain fraction is equal to 4,140. When the fraction was reduced, the result was 7/13. What was the original fraction?

Original fraction was [tex]\dfrac{7\cdot k}{13\cdot k}[/tex] where [tex]k[/tex] is a reduced common factor. We know that:

[tex]7k+13k=4140\\\\20k=4140\qquad|:20\\\\\boxed{k=207}[/tex]

so original fraction:

[tex]\dfrac{7\cdot k}{13\cdot k}=\dfrac{7\cdot 207}{13\cdot 207}=\boxed{\dfrac{1449}{2691}}[/tex]