Ta có: \(\left(\frac{8}{1.9}+\frac{8}{9.17}+\frac{8}{17.25}+...+\frac{8}{49.57}\right)+2\left(x-1\right)=\frac{2x+7}{3}+\frac{5x-8}{4}\)

\(\Leftrightarrow1-\frac{1}{9}+\frac{1}{9}-\frac{1}{17}+\frac{1}{17}-\frac{1}{25}+....+\frac{1}{49}-\frac{1}{57}+2x-2=\frac{8x+28+15x-24}{12}\)

\(\Leftrightarrow1-\frac{1}{57}+2x-2=\frac{23x+4}{12}\)

\(\Leftrightarrow2x-\frac{58}{57}=\frac{23x+4}{12}\)

\(\Leftrightarrow24x-\frac{232}{19}=23x+4\)

\(\Leftrightarrow x=\frac{308}{19}\)

a: \(\Leftrightarrow\left(1-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{17}+...+\dfrac{1}{49}-\dfrac{1}{57}\right)+2x-2=\dfrac{2}{3}x+\dfrac{7}{3}+\dfrac{5}{4}x-2\)

\(\Leftrightarrow\dfrac{56}{57}+2x-2=\dfrac{23}{12}x+\dfrac{1}{3}\)

=>1/12x=77/57

=>x=308/19

b: =>(x^2-4)(x^2-10)=72

=>x^4-14x^2+40-72=0

=>x^4-14x^2-32=0

=>(x^2-16)(x^2+2)=0

=>x^2-16=0

=>x^2=16

=>x=4 hoặc x=-4

G=6(6/1.7+6/7.13+6/13.19+..+6/n(n+6) )

=6(1-1/7+1/7-1/13+1/13-1/19+....+1/n-1/n+6)

=6(1-n/n+6)

=6.6/n+6

=36/n+6

vậy G=36/n+6

\(\frac{5}{1.7}+\frac{5}{7.13}+\frac{5}{13.19}+...+\frac{5}{2017.2023}\)

\(=5.\frac{1}{6}.\left(\frac{6}{1.7}+\frac{6}{7.13}+\frac{6}{13.19}+...+\frac{6}{2017.2023}\right)\)

\(=\frac{5}{6}.\left(1-\frac{1}{7}+\frac{1}{7}-\frac{1}{13}+\frac{1}{13}-\frac{1}{19}+...+\frac{1}{2017}-\frac{1}{2023}\right)\)

\(=\frac{5}{6}.\left(1-\frac{1}{2023}\right)\)

\(=\frac{5}{6}.\frac{2022}{2023}\)

\(=\frac{1685}{2023}\)

\(\frac{5}{1.7}+\frac{5}{7.13}+\frac{5}{13.19}+...+\frac{5}{2017.2023}\)

\(=\frac{5.6}{1.7.6}+\frac{5.6}{7.13.6}+\frac{5.6}{13.19.6}+.....+\frac{5.6}{2017.2023.6}\)

\(=\frac{5}{6}.\left(\frac{6}{1.7}+\frac{6}{7.13}+\frac{6}{13.19}+...+\frac{6}{2017.2023}\right)\)

\(=\frac{5}{6}.\left(1-\frac{1}{7}+\frac{1}{7}-\frac{1}{13}+\frac{1}{13}-\frac{1}{19}+...+\frac{1}{2017}-\frac{1}{2023}\right)\)

\(=\frac{5}{6}.\left(1-\frac{1}{2023}\right)\)

\(=\frac{5}{6}.\frac{2022}{2023}\)

\(=\frac{1685}{2023}\)