The value of $\frac{\frac{5}{2}-\frac{3}{7}\times1\frac{4}{5}\div3\frac{6}{7}}{\frac{3}{2}+1\frac{2}{5}\div 3\frac{1}{2} \times 1\frac{1}{4}}$ is:

$1\frac{3}{20}$

$\frac{\frac{5}{2}-\frac{3}{7}\times1\frac{4}{5}\div3\frac{6}{7}}{\frac{3}{2}+1\frac{2}{5}\div 3\frac{1}{2} \times 1\frac{1}{4}}$ 

a² + b² = (a + b)(a - b)

= \(\frac{500^2 - (-250)^2}{375^2 - 125^2}\)

= \(\frac{250 \times 750}{500 \times 250}\)

= \(\frac{750}{500}\) = \(\frac{3}{2}\)