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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

#### 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,

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

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

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

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

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

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

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

Is there an error in this question or solution?

#### 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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