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Simplify : 3 X 2 − X − 2 X 2 − 7 X + 12 ÷ 3 X 2 − 7 X − 6 X 2 − 4 - SSC (English Medium) Class 8 - Mathematics

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Question

Simplify :

\[\frac{3 x^2 - x - 2}{x^2 - 7x + 12} \div \frac{3 x^2 - 7x - 6}{x^2 - 4}\]

Solution

It is known that,

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

\[\  \frac{3 x^2 - x - 2}{x^2 - 7x + 12} \div \frac{3 x^2 - 7x - 6}{x^2 - 4}\] 

\[ = \frac{3 x^2 - 3x + 2x - 2}{x^2 - 4x - 3x + 12}   \div   \frac{3 x^2 - 9x + 2x - 6}{\left( x \right)^2 - \left( 2 \right)^2}\] 

\[ = \frac{3x\left( x - 1 \right) + 2\left( x - 1 \right)}{x\left( x - 4 \right) - 3\left( x - 4 \right)} \div \frac{3x\left( x - 3 \right) + 2\left( x - 3 \right)}{\left( x + 2 \right)\left( x - 2 \right)}\] 

\[ = \frac{\left( 3x + 2 \right)\left( x - 1 \right)}{\left( x - 3 \right)\left( x - 4 \right)} \div \frac{\left( 3x + 2 \right)\left( x - 3 \right)}{\left( x + 2 \right)\left( x - 2 \right)}\] 

\[ = \frac{\left( 3x + 2 \right)\left( x - 1 \right)}{\left( x - 3 \right)\left( x - 4 \right)} \times \frac{\left( x + 2 \right)\left( x - 2 \right)}{\left( 3x + 2 \right)\left( x - 3 \right)}\] 

\[ = \frac{\left( x - 1 \right)\left( x + 2 \right)\left( x - 2 \right)}{\left( x - 4 \right)\left( x - 3 \right)\left( x - 3 \right)}\]

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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: 5 | Page no. 33
Solution Simplify : 3 X 2 − X − 2 X 2 − 7 X + 12 ÷ 3 X 2 − 7 X − 6 X 2 − 4 Concept: Factors of A3 - B3.
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