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प्रश्न
Simplify:
\[\frac{3 x^2 - x - 2}{x^2 - 7x + 12} \div \frac{3 x^2 - 7x - 6}{x^2 - 4}\]
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)`
संबंधित प्रश्न
Simplify:
\[\frac{a^2 + 10a + 21}{a^2 + 6a - 7} \times \frac{a^2 - 1}{a + 3}\]
Simplify:
\[\frac{4 x^2 - 11x + 6}{16 x^2 - 9}\]
Simplify:
\[\frac{1 - 2x + x^2}{1 - x^3} \times \frac{1 + x + x^2}{1 + x}\]
Factorise:
x3 − 64y3
Factorise:
343a3 − 512b3
Simplify:
(x + y)3 − (x − y)3
Simplify:
(3a + 5b)3 − (3a − 5b)3
Simplify:
p3 − (p + 1)3
Factorise: 54p3 - 250q3.
Factorise the following:
27x3 – 8y3
