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:
\[\frac{m^2 - n^2}{\left( m + n \right)^2} \times \frac{m^2 + mn + n^2}{m^3 - n^3}\]
Simplify:
\[\frac{a^2 + 10a + 21}{a^2 + 6a - 7} \times \frac{a^2 - 1}{a + 3}\]
Simplify:
\[\frac{x^2 - 5x - 24}{\left( x + 3 \right)\left( x + 8 \right)} \times \frac{x^2 - 64}{\left( x - 8 \right)^2}\]
Factorise:
x3 − 64y3
Factorise:
27m3 − 216n3
Factorise:
125y3 − 1
Simplify:
(a + b)3 − a3 − b3
Simplify:
p3 − (p + 1)3
Factorise: 27p3 - 125q3.
Simplify: (2x + 3y)3 - (2x - 3y)3
