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This question belongs to Arithmetic Ability Simplification
Simplification
?

$$\frac{{{{\left( {a - b} \right)}^2} - {{\left( {a + b} \right)}^2}}}{{ - 4a}}{\text{ = }}\frac{x}{y}$$     On simplifying the given equations, which of the following equations will be obtained ?

Answer & Solution
Correct Answer: Option D
$$\eqalign{ & \frac{{{{\left( {a - b} \right)}^2} - {{\left( {a + b} \right)}^2}}}{{ - 4a}}{\text{ = }}\frac{x}{y} \cr & \Rightarrow \frac{{\left( {{a^2} + {b^2} - 2ab} \right) - \left( {{a^2} + {b^2} + 2ab} \right)}}{{ - 4a}} = \frac{x}{y} \cr & \Rightarrow \frac{{ - 4ab}}{{ - 4a}} = \frac{x}{y} \cr & \Rightarrow b = \frac{x}{y} \cr & \Rightarrow x = yb \cr} $$
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