Simplify the following expression- a - ab-a - b ab-a - b - a -a2 - b2-a2 - b2

(a+aba b)(aba b a)=a^2b^2(a b)^2 a^2=a^2b^2 a^2 b^2+2ab(a b)^2=a^3(2b a)(a b)^2 (a+aba b)(aba b a):a^2+b^2a^2 b^2=a^3(2b a)(a b)^2×a^2 b^2a^2+b^2=a^3( ...

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Byju's Answer

Standard VII

Mathematics

Changing Scale (Including Flags)

Simplify the ...

Question

Simplify the following expression:
$(a + \frac{a b}{a - b}) (\frac{a b}{a - b} - a) : \frac{a^{2} + b^{2}}{a^{2} - b^{2}}$

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Solution

$(a + \frac{a b}{a - b}) (\frac{a b}{a - b} - a) = \frac{a^{2} b^{2}}{(a - b)^{2}} - a^{2} = a^{2} \frac{b^{2} - a^{2} - b^{2} + 2 a b}{(a - b)^{2}} = \frac{a^{3} (2 b - a)}{(a - b)^{2}}$
$(a + \frac{a b}{a - b}) (\frac{a b}{a - b} - a) : \frac{a^{2} + b^{2}}{a^{2} - b^{2}} = \frac{a^{3} (2 b - a)}{(a - b)^{2}} \times \frac{a^{2} - b^{2}}{a^{2} + b^{2}} = \frac{a^{3} (2 b - a) (a + b)}{(a + b) (a^{2} + b^{2})}$

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Simplify the following expression:(a+aba−b)(aba−b−a):a2+b2a2−b2

(a+aba−b)(aba−b−a)=a2b2(a−b)2−a2=a2b2−a2−b2+2ab(a−b)2=a3(2b−a)(a−b)2(a+aba−b)(aba−b−a):a2+b2a2−b2=a3(2b−a)(a−b)2×a2−b2a2+b2=a3(2b−a)(a+b)(a+b)(a2+b2)

Simplify the following expression:
$(a + \frac{a b}{a - b}) (\frac{a b}{a - b} - a) : \frac{a^{2} + b^{2}}{a^{2} - b^{2}}$