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Question

Simplify: $$ \cfrac{\left ( 3\tfrac{2}{3} \right )^{2}-\left ( 2\tfrac{1}{2} \right )^{2}}{\left ( 4\tfrac{3}{4} \right )^{2}-\left ( 3\tfrac{1}{3} \right )^{2}}\div \cfrac{3\tfrac{2}{3}-2\tfrac{1}{2}}{4\tfrac{3}{4}-3\tfrac{1}{3}}$$


A
7497
loader
B
5297
loader
C
74107
loader
D
6497
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Solution

The correct option is A $$\displaystyle \frac{74}{97}$$
Given $$ \cfrac{\left ( 3\tfrac{2}{3} \right )^{2}-\left ( 2\tfrac{1}{2} \right )^{2}}{\left ( 4\tfrac{3}{4} \right )^{2}-\left ( 3\tfrac{1}{3} \right )^{2}}\div \cfrac{3\tfrac{2}{3}-2\tfrac{1}{2}}{4\tfrac{3}{4}-3\tfrac{1}{3}}$$

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


$$=\cfrac{\left ( \dfrac{11}{3}+\dfrac{5}{2} \right )\left ( \dfrac{11}{3}-\dfrac{5}{2} \right)}{\left ( \dfrac{19}{4}+\dfrac{10}{3} \right )\left ( \dfrac{19}{4}-\dfrac{10}{3} \right )}\times \cfrac{\left ( \dfrac{19}{4}-\dfrac{10}{3} \right )}{\left ( \dfrac{11}{3}-\dfrac{5}{2} \right )}$$



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


$$=\cfrac{\dfrac{37}{6}}{\dfrac{97}{12}}$$


$$=\cfrac{37\times2}{97}=\cfrac{74}{97}$$

Mathematics

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