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प्रश्न
Simplify:
\[\frac{3 x^2 - x - 2}{x^2 - 7x + 12} \div \frac{3 x^2 - 7x - 6}{x^2 - 4}\]
सरल रूप दीजिए
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उत्तर
It is known that,
a3 − b3 = (a − b)(a2 + ab + b2)
`(3x^2 - x - 2)/(x^2 - 7x + 12) xx (x^2 - 4)/(3x^2 - 7x - 6)`
= `(3x^2 - 3x + 2x - 2)/(x^2 - 4x - 3x + 12) xx (x^2 - 2^2)/(3x^2 - 9x + 2x - 6)`
= `(3x(x - 1) + 2(x - 1))/(x(x - 4) - 3(x - 4)) xx ((x + 2)(x - 2))/(3x(x - 3) + 2(x - 3))`
= `((x - 1)(3x + 2))/((x - 4)(x - 3)) xx ((x + 2)(x - 2))/((x - 3)(3x + 2))`
= `((x - 1)(x + 2)(x - 2))/((x - 4)(x - 3)^2)`
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