\(\frac{2}{3}\div\frac{x}{5}+\frac{5}{7}=\frac{2}{7}\div\frac{3}{5}+\frac{10}{9}\)
\(\frac{2}{3}\div\frac{x}{5}+\frac{5}{7}=\frac{10}{21}+\frac{10}{9}\)
\(\frac{2}{3}\div\frac{x}{5}+\frac{5}{7}=\frac{300}{189}\)
\(\frac{2}{3}\div\frac{x}{5}=\frac{300}{189}-\frac{5}{7}\)
\(\frac{2}{3}\div\frac{x}{5}=\frac{55}{63}\)
\(\frac{x}{5}=\frac{2}{3}\div\frac{55}{63}\)
\(\frac{x}{5}=\frac{42}{55}\)
\(x=42\div\left(55\div5\right)=\frac{42}{11}\)
\(\frac{2}{3}:\frac{x}{5}+\frac{5}{7}=\frac{2}{7}:\frac{3}{5}+\frac{10}{9}\)
\(\Leftrightarrow\frac{10}{3x}=\frac{10}{21}+\frac{10}{9}-\frac{5}{7}\)
\(\Leftrightarrow\frac{10}{3x}=\frac{55}{63}\)
\(\Leftrightarrow10\times63=55\times3x\)
\(\Leftrightarrow630=165\times x\)
\(\Leftrightarrow x=\frac{42}{11}\)
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\(\frac{2}{3}:\frac{x}{5}+\frac{5}{7}=\frac{2}{7}:\frac{3}{5}+\frac{10}{9}\)
\(\Rightarrow\frac{2}{3}.\frac{5}{x}+\frac{5}{7}=\frac{2}{7}.\frac{5}{3}+\frac{10}{9}\)
\(\Rightarrow\frac{10}{3x}+\frac{5}{7}=\frac{10}{21}+\frac{10}{9}=\frac{100}{63}\)
\(\Rightarrow\frac{10}{3x}=\frac{100}{63}-\frac{5}{7}=\frac{55}{63}\)
\(\Rightarrow630=165x\)
\(\Rightarrow x=\frac{42}{11}\)