Advertisements
Advertisements
Question
Simplify:
`(1 - 2x + x^2)/(1 - x^3) xx (1 + x + x^2)/(1 + x)`
Advertisements
Solution
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)`
RELATED QUESTIONS
Simplify:
\[\frac{4 x^2 - 11x + 6}{16 x^2 - 9}\]
Simplify:
\[\frac{a^3 - 27}{5 a^2 - 16a + 3} \div \frac{a^2 + 3a + 9}{25 a^2 - 1}\]
Factorise:
x3 − 64y3
Factorise:
27m3 − 216n3
Factorise:
64x3 − 729y3
Factorise:
`16a^3 - 128/b^3`
Simplify:
(x + y)3 − (x − y)3
Simplify:
(3a + 5b)3 − (3a − 5b)3
Simplify:
(3xy − 2ab)3 − (3xy + 2ab)3
Simplify: (2x + 3y)3 - (2x - 3y)3
