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If x + y = 2a, then the value of$$\frac{a}{{x - a}} + \frac{a}{{y - a}}\,{\text{is = ?}}$$

If x + y = 2a, then the value of$$\frac{a}{{x - a}} + \frac{a}{{y - a}}\,{\text{is = ?}}$$ Correct Answer 0

$$\eqalign{ & {\text{Given, }} \cr & x + y = 2a \cr & \therefore \frac{a}{{x - a}} + \frac{a}{{y - a}} \cr & = \frac{{a\left( {y - a} \right) + a\left( {x - a} \right)}}{{\left( {x - a} \right)\left( {y - a} \right)}} \cr & = \frac{{ay - {a^2} + ax - {a^2}}}{{\left( {x - a} \right)\left( {y - a} \right)}} \cr & = \frac{{a\left( {x + y} \right) - 2{a^2}}}{{\left( {x - a} \right)\left( {y - a} \right)}} \cr & = \frac{{a.2a - 2{a^2}}}{{\left( {x - a} \right)\left( {y - a} \right)}} \cr & = \frac{{2{a^2} - 2{a^2}}}{{\left( {x - a} \right)\left( {y - a} \right)}} \cr & = 0 \cr} $$

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