\(\frac{7}{5}=\frac{2x+1}{3x+5}\)

\(\Leftrightarrow7\left(3x+5\right)=5\left(2x+1\right)\)

\(21x+35=10x+5\)

\(21x+35-10x-5=0\)

\(11x+30=0\)

\(11x=-30\)

\(x=-\frac{30}{11}\)

B1: Quy đồng hai phân số 
\(\frac{7}{5}\)=\(\frac{2x+1}{3x+5}\)

\(\Leftrightarrow\)\(\frac{7.\left(3x+5\right)}{5.\left(3x+5\right)}\)= \(\frac{5.\left(2x+1\right)}{5.\left(3x+5\right)}\)

B2: khử mẫu đi 

\(\Rightarrow\)7(3x+5) = 5(2x+1)

B3: Tính phương trình 

\(\Leftrightarrow\)21x+35=10x+5

\(\Leftrightarrow\)21x+35-10x+5=0

\(\Leftrightarrow\)11x+40=0

\(\Leftrightarrow\)11x = -40

\(\Leftrightarrow\) x = \(\frac{-40}{11}\)

Vậy x = \(\frac{-40}{11}\) là nghiệm của phương trình đã cho trên

\(\left(7x-8\right)^2=36\)

\(\left(7x-8\right)^2=6^2=\left(-6\right)^2\)

\(\Rightarrow7x-8=6\text{ hoặc }7x-8=-6\)

              \(7x=14\)               \(7x=2\)

                \(x=2\)                    \(x=\frac{2}{7}\)

Ta có :

\(A=\frac{9}{1}+\frac{8}{2}+\frac{7}{3}+...+\frac{1}{9}\)

\(A=9+\frac{8}{2}+\frac{7}{3}+...+\frac{1}{9}\)

\(A=\left(\frac{8}{2}+1\right)+\left(\frac{7}{3}+1\right)+...+\left(\frac{1}{9}+1\right)+1\)

\(A=\frac{10}{2}+\frac{10}{3}+...+\frac{10}{9}+\frac{10}{10}\)

\(A=10\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{10}\right)\)

\(\Rightarrow\frac{A}{B}=\frac{10\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{10}\right)}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{10}}=10\)

Bài 2 :

\(\frac{1}{2.3}x+\frac{1}{3.4}x+\frac{1}{4.5}x+...+\frac{1}{49.50}x=1\)

\(x\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{49.50}\right)=1\)

\(x\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{4}+...+\frac{1}{49}-\frac{1}{50}\right)=1\)

\(x\left(\frac{1}{2}-\frac{1}{50}\right)=1\)

\(\left(\frac{25}{50}-\frac{1}{50}\right)x=1\)

\(\frac{12}{25}x=1\)

\(x=1:\frac{12}{25}\)

\(x=\frac{25}{12}\)

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