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Simplify : 1 − 2 X + X 2 1 − X 3 × 1 + X + X 2 1 + X - SSC (English Medium) Class 8 - Mathematics

Question

Simplify :

$\frac{1 - 2x + x^2}{1 - x^3} \times \frac{1 + x + x^2}{1 + x}$

Solution

It is known that,

$a^2 - b^2 = \left( a + b \right)\left( a - b \right) ; a^3 - b^3 = \left( a - b \right)\left( a^2 + ab + b^2 \right)$

$\ \frac{1 - 2x + x^2}{1 - x^3} \times \frac{1 + x + x^2}{1 + x}$

$= \frac{1 - x - x + x^2}{\left( 1 \right)^3 - \left( x \right)^3} \times \frac{1 + x + x^2}{1 + x}$

$= \frac{1\left( 1 - x \right) - x\left( 1 - x \right)}{\left( 1 - x \right)\left\{ \left( 1 \right)^2 + \left( 1 \right) \times \left( x \right) + \left( x \right)^2 \right\}} \times \frac{\left( 1 + x + x^2 \right)}{1 + x}$

$= \frac{\left( 1 - x \right)\left( 1 - x \right)}{\left( 1 - x \right)\left( 1 + x + x^2 \right)} \times \frac{\left( 1 + x + x^2 \right)}{\left( 1 + x \right)}$

$= \frac{1 - x}{1 + x}$

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APPEARS IN

Balbharati Solution for Balbharati Class 8 Mathematics (2019 to Current)
Chapter 6: Factorisation of Algebraic expressions
Practice Set 6.4 | Q: 8 | Page no. 33
Solution Simplify : 1 − 2 X + X 2 1 − X 3 × 1 + X + X 2 1 + X Concept: Factors of A3 - B3.
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