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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

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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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