Question

Simplify: $\frac{{\left(3\frac{2}{3}\right)}^2-{\left(2\frac{1}{2}\right)}^2}{{\left(4\frac{3}{4}\right)}^2-{\left(3\frac{1}{3}\right)}^2}÷\frac{3\frac{2}{3}-2\frac{1}{2}}{4\frac{3}{4}-3\frac{1}{3}}$

• A. $\frac{74}{97}$
• B. $\frac{52}{97}$
• C. $\frac{74}{107}$
• D. $\frac{64}{97}$

Answer 1

The correct option is A $\frac{74}{97}$

Given $\frac{{\left(3\frac{2}{3}\right)}^2-{\left(2\frac{1}{2}\right)}^2}{{\left(4\frac{3}{4}\right)}^2-{\left(3\frac{1}{3}\right)}^2}÷\frac{3\frac{2}{3}-2\frac{1}{2}}{4\frac{3}{4}-3\frac{1}{3}}$

$=\frac{{\left(\frac{11}{3}\right)}^2-{\left(\frac{5}{2}\right)}^2}{{\left(\frac{19}{4}\right)}^2-{\left(\frac{10}{3}\right)}^2}\times \frac{(\frac{19}{4}-\frac{10}{3})}{(\frac{11}{3}-\frac{5}{2})}$

$=\frac{(\frac{11}{3}+\frac{5}{2})(\frac{11}{3}-\frac{5}{2})}{(\frac{19}{4}+\frac{10}{3})(\frac{19}{4}-\frac{10}{3})}\times \frac{(\frac{19}{4}-\frac{10}{3})}{(\frac{11}{3}-\frac{5}{2})}$

$=\frac{\frac{22+15}{6}}{\frac{57+40}{12}}$

$=\frac{\frac{37}{6}}{\frac{97}{12}}$

$=\frac{37\times 2}{97}=\frac{74}{97}$