Question

\(\frac{2}{3}\):\(\frac{x}{5}\)+\(\frac{5}{7}\)= \(\frac{2}{7}\): \(\frac{3}{5}\)+ \(\frac{10}{9}\)

Answer 1

\(;\frac{2}{3}.\frac{5}{x}+\frac{5}{7}=\frac{10}{21}+\frac{10}{9}\)

\(;\frac{10}{3x}+\frac{5}{7}=\frac{100}{63}\)

\(;\frac{10}{3x}=\frac{100}{63}-\frac{5}{7}=\frac{55}{63}\)

\(;3x=10:\frac{55}{63}=\frac{126}{11}\)

\(;x=\frac{126}{11}:3=\frac{42}{11}\)

Answer 2

\(\frac{2}{3}:\frac{x}{5}+\frac{5}{7}=\frac{2}{7}:\frac{3}{5}+\frac{10}{9}\)

→ \(\frac{2}{3}:\frac{x}{5}+\frac{5}{7}=\frac{10}{21}+\frac{10}{9}=\frac{100}{63}\)

→ \(\frac{2}{3}:\frac{x}{5}=\frac{100}{63}-\frac{5}{7}\)

→ \(\frac{2}{3}:\frac{x}{5}=\frac{55}{63}\)

→ \(\frac{x}{5}=\frac{2}{3}:\frac{55}{63}\)

→ \(\frac{x}{5}=\frac{42}{55}\)

→ \(x:5=\frac{42}{55}\)

→ x = \(\frac{42}{55}\) . 5

→ x = \(\frac{42}{11}\) = 3,8

→ x : 5 = \(\frac{42}{55}\)

→ \(\frac{x}{5}=\frac{42}{55}\)