= 13/15 + 13/35 + 13/63 + 13/99
= 13/ 3×5 + 13/5×7 + 13/7×9 + 13/9×11
= 13 x 1/2( 1/3 – 1/5 + 1/5 – 1/7 +1/7 – 1/9 +1/9 – 1/11)
= 13/2 x ( 1/3 – 1/11)
= 13/2 x 8/33 = 104/66=52/33

\(D=\frac{13}{15}+\frac{13}{35}+\frac{13}{63}+\frac{13}{99}\)

\(D=\frac{13}{3}\times5+\frac{13}{5}\times7+\frac{13}{7}\times9+\frac{13}{9}\times11\)

\(D=13\times\frac{1}{2}\left(\frac{1}{3}-\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}\right)\)

\(D=\frac{13}{2}\times\left(\frac{1}{3}-\frac{1}{11}\right)\)

\(D=\frac{13}{2}\times\frac{8}{33}=\frac{104}{66}=\frac{52}{33}\)

\(D=\frac{52}{33}\)

(131313/151515+ 131313/353535+131313/636363+131313/999999)*33

=(13/15+13/35+13/63+13/99)*33

=52/33*33

=52

131313 + 131313 + 131313 + 131313 / 151515 + 353535 + 6363636 + 999999

= 131313 x 4 / 10101 x ( 15 + 35 + 63 + 99)

= 10101 x 13 x 4 / 10101 x 212

= 10101 x 52 / 10101 x 212

= 13/53

\(\dfrac{2}{3}x-70.\dfrac{10}{11}:\left(\dfrac{131313}{151515}+\dfrac{131313}{353535}+\dfrac{131313}{636363}+\dfrac{131313}{999999}\right)=-5\)

\(\dfrac{2}{3}x-70.\dfrac{10}{11}:\left(\dfrac{13}{15}+\dfrac{13}{35}+\dfrac{13}{63}+\dfrac{13}{99}\right)=-5\)

\(\dfrac{2}{3}x-70.\dfrac{10}{11}:\left(\dfrac{13}{3.5}+\dfrac{13}{5.7}+\dfrac{13}{7.9}+\dfrac{13}{9.11}\right)=-5\)

\(\dfrac{2}{3}x-70.\dfrac{10}{11}:\left[\dfrac{13}{2}.\left(\dfrac{2}{3.5}+\dfrac{2}{5.7}+\dfrac{2}{7.9}+\dfrac{2}{9.11}\right)\right]=-5\)

\(\dfrac{2}{3}x-70.\dfrac{10}{11}:\left[\dfrac{13}{2}.\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{11}\right)\right]=-5\)

\(\dfrac{2}{3}x-70.\dfrac{10}{11}:\left[\dfrac{13}{2}.\left(\dfrac{1}{3}-\dfrac{1}{11}\right)\right]=-5\)

\(\dfrac{2}{3}x-70.\dfrac{10}{11}:\left[\dfrac{13}{2}.\dfrac{8}{33}\right]=-5\)

\(\dfrac{2}{3}x-\dfrac{700}{11}:\dfrac{52}{33}=-5\)

\(\dfrac{2}{3}x-\dfrac{525}{13}=-5\)

\(\dfrac{2}{3}x=-5+\dfrac{525}{13}=\dfrac{460}{13}\)

\(x\) = \(\dfrac{460}{13}:\dfrac{2}{3}=\dfrac{690}{13}\).

\(\Leftrightarrow\frac{2}{3}x-\frac{780}{11}:\left(\frac{13}{15}+\frac{13}{35}+\frac{13}{63}+\frac{13}{99}\right)=-5\)

\(\Leftrightarrow\frac{2}{3}x-40=0\)

\(\Leftrightarrow x=60\)

\(=\frac{13\times10101}{15\times10101}+\frac{13\times10101}{35\times10101}+\frac{13\times10101}{63\times10101}+\frac{13\times10101}{99\times10101}\)

\(=\frac{13}{15}+\frac{13}{35}+\frac{13}{63}+\frac{13}{99}=\frac{13}{2}\times\left(\frac{2}{3\times5}+\frac{2}{5\times7}+\frac{3}{7\times9}+\frac{2}{9\times11}\right)\)

\(=\frac{13}{2}\times\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}\right)=\frac{13}{2}\times\left(\frac{1}{3}-\frac{1}{11}\right)=\frac{13}{2}\times\frac{8}{33}=\frac{52}{33}\)

\(\frac{13.10101}{15.10101}\)+\(\frac{13.10101}{15.10101}\)+\(\frac{13.10101}{63.10101}\)+ \(\frac{13.10101}{99.10101}\)= \(\frac{13}{15}\) +   \(\frac{13}{15}\) + \(\frac{13}{63}\)+  \(\frac{13}{99}\) =\(2\frac{82}{1155}\)

Kết quả của phép tính trên là \(\frac{52}{33}.\)