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Factors of Algebraic Expressions and Factorisation

Simplify:ii a...

Question

Simplify:

$(i i)$ $(a + b)^{- 1} . (a^{- 1} + b^{- 1})$

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Solution

Simplifying the given expression Given,

$(a + b)^{- 1} . (a^{- 1} + b^{- 1})$

It can be simplified as :

$(a + b)^{- 1} . (a^{- 1} + b^{- 1}) = \frac{1}{a + b} \times (\frac{1}{a} + \frac{1}{b})$

$[∵ x^{- 1} = \frac{1}{x}]$

$= \frac{1}{a + b} \times \frac{b + a}{a b}$ [Taking LCM]

= $\frac{1}{a + b} \times \frac{a + b}{a b} = \frac{1}{a b}$

Hence, the simplified value is $\frac{1}{a b}$

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Similar questions

$a b - a - b + 1 = ? (a) (a - 1) (b - 1) (b) (1 - a) (1 - b) (c) (a - 1) (1 - b) (d) (1 - a) (b - 1)$

$1 - 2 a b - (a^{2} + b^{2}) = ? (a) (1 + a - b) (1 + a + b) (b) (1 + a + b) (1 - a + b) (c) (1 + a + b) (1 - a - b) (d) (1 + a - b) (1 - a + b)$

Q. Tick (✓) the correct answer:
ab − a − b + 1 = ?
(a) (a − 1)(b − 1)
(b) (1 − a)(1 − b)
(c) (a − 1)(1 − b)
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Q. Prove that:

(i)

\frac{a + b + c}{a^{- 1} b^{- 1} + b^{- 1} c^{- 1} + c^{- 1} a^{- 1}} = a b c

{(a^{- 1} + b^{- 1})}^{- 1} = \frac{a b}{a + b}

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Factors of Algebraic Expressions and Factorisation

Standard VIII Mathematics

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