The lowest form of a-b-a b-2-a-b if a b-1A- a2-b2-a-bB- 2 ab - a - b C- a2-b2-a-bD- ab

The correct option is A (a^2 + b^2)/(a + b) Here the algebraic fraction is (a + b)/ab 2/(a + b) It can be reduced to ((a + b)^2 2ab)/(ab)× (a + b) Since ab ...

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Standard VIII

Mathematics

Multiplication of Monomials

The lowest fo...

Question

The lowest form of $\frac{(a + b)}{a b} - \frac{2}{(a + b)}$ if ab=1.

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$\frac{(a^{2} - b^{2})}{(a - b)}$

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$\frac{(a^{2} + b^{2})}{(a + b)}$

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2ab-(a+b)

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Solution

The correct option is C
$\frac{(a^{2} + b^{2})}{(a + b)}$

Here the algebraic fraction is $\frac{(a + b)}{a b} - \frac{2}{(a + b)}$

It can be reduced to $\frac{((a + b)^{2} - 2 a b)}{(a b) \times (a + b)}$

Since ab=1, it'll be again reduced to $\frac{((a + b)^{2} - 2 a b)}{(a + b)}$

[we have known that $(a + b)^{2} = a^{2} + 2 a b + b^{2}$ ]

So, the reduced form is $\frac{(a^{2} + b^{2})}{(a + b)}$

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The lowest form of (a + b)ab − 2(a + b) if ab=1.

The correct option is C (a2 + b2)(a + b) Here the algebraic fraction is (a + b)ab − 2(a + b) It can be reduced to ((a + b)2 − 2ab)(ab)×(a + b) Since ab=1, it'll be again reduced to ((a + b)2 − 2ab)(a + b) [we have known that (a + b)2 = a2 + 2ab + b2 ] So, the reduced form is (a2 + b2)(a + b)

The lowest form of $\frac{(a + b)}{a b} - \frac{2}{(a + b)}$ if ab=1.