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प्रश्न
Simplify:
\[\frac{m^2 - n^2}{\left( m + n \right)^2} \times \frac{m^2 + mn + n^2}{m^3 - n^3}\]
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उत्तर
We know that,
a3 + b3 = (a + b)(a2 − ab + b2)
a3 − b3 = (a − b)(a2 + ab + b2)
a2 − b2= (a + b) (a − b)
\[\frac{m^2 - n^2}{\left( m + n \right)^2} \times \frac{m^2 + mn + n^2}{m^3 - n^3}\]
\[ = \frac{\left( m + n \right)\left( m - n \right)}{\left( m + n \right)\left( m + n \right)} \times \frac{\left( m^2 + mn + n^2 \right)}{\left( m - n \right)\left( m^2 + mn + n^2 \right)}\]
\[= \frac{1}{m + n}\]
संबंधित प्रश्न
Simplify:
\[\frac{8 x^3 - 27 y^3}{4 x^2 - 9 y^2}\]
Simplify:
\[\frac{a^2 + 10a + 21}{a^2 + 6a - 7} \times \frac{a^2 - 1}{a + 3}\]
Simplify:
\[\frac{3 x^2 - x - 2}{x^2 - 7x + 12} \div \frac{3 x^2 - 7x - 6}{x^2 - 4}\]
Simplify:
\[\frac{4 x^2 - 11x + 6}{16 x^2 - 9}\]
Simplify:
`(1 - 2x + x^2)/(1 - x^3) xx (1 + x + x^2)/(1 + x)`
Factorise:
8p3 −\[\frac{27}{p^3}\]
Factorise:
343a3 − 512b3
Factorise:
`16a^3 - 128/b^3`
Factorise: x3 - 8y3
Factorise: `a^3 - 1/(a^3)`
