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प्रश्न
Simplify:
`(1 - 2x + x^2)/(1 - x^3) xx (1 + x + x^2)/(1 + x)`
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उत्तर
It is known that,
a2 − b2 = (a + b) (a − b)
a3 − b3 = (a − b)(a2 + ab + b2)
`(1 - 2x + x^2)/(1 - x^3) xx (1 + x + x^2)/(1 + x)`
= `(1 - x - x + x^2)/((1)^3 - (x)^3) xx (1 + x + x^2)/(1 + x)`
= `(1(1 - x) - x(1 - x))/((1 - x){(1)^2 + (1) xx (x) + (x)^2}) xx ((1 + x + x^2))/(1 + x)`
= `((1 - x) (1 - x))/((1 - x) (1 + x + x^2)) xx ((1 + x + x^2))/((1 + x))`
= `(1 - x)/(1 + x)`
संबंधित प्रश्न
Simplify:
\[\frac{8 x^3 - 27 y^3}{4 x^2 - 9 y^2}\]
Simplify:
\[\frac{x^2 - 5x - 24}{\left( x + 3 \right)\left( x + 8 \right)} \times \frac{x^2 - 64}{\left( x - 8 \right)^2}\]
Simplify:
\[\frac{3 x^2 - x - 2}{x^2 - 7x + 12} \div \frac{3 x^2 - 7x - 6}{x^2 - 4}\]
Factorise:
y3 − 27
Factorise:
27m3 − 216n3
Factorise:
8p3 −\[\frac{27}{p^3}\]
Factorise:
64x3 − 729y3
Factorise: x3 - 8y3
Factorise: `a^3 - 1/(a^3)`
Factorise the following:
27x3 – 8y3
