Advertisements
Advertisements
Question
Simplify `(x^3 - y^3)/(3x^2 + 9xy + 6y^2) xx (x^2 + 2xy + y^2)/(x^2 - y^2)`
Advertisements
Solution
x3 – y3 = (x – y) (x2 + xy + y2)
x2 + 2xy + y2 = (x + y) (x + y)
3x2 + 9xy + 6y2 = 3(x2 + 3xy + 2y2)
= 3 (x + 2y) (x + y)
(x2 – y2) = (x + y) (x – y)
`(x^3 - y^3)/(3x^2 + 9xy + 6y^2) xx (x^2 + 2xy + y^2)/(x^2 - y^2)`
= `((x - y)(x^2 + xy + y^2))/(3(x + 2y)(x + y)) xx ((x + y)(x + y))/((x + y)(x - y))`
= `(x^2 + xy + y^2)/(3(x + 2y))`
APPEARS IN
RELATED QUESTIONS
Reduce the following rational expression to its lowest form
`(x^2 - 11x + 18)/(x^2 - 4x + 4)`
Reduce the following rational expression to its lowest form
`(9x^2 + 81x)/(x^3 + 8x^2 - 9x)`
Find the excluded values, of the following expression
`y/(y^2 - 25)`
Find the excluded values, of the following expression
`(x^3 - 27)/(x^3 + x^2 - 6x)`
Identify rational expression should be subtracted from `(x^2 + 6x + 8)/(x^3 + 8)` to get `3/(x^2 - 2x + 4)`
Pari needs 4 hours to complete the work. His friend Yuvan needs 6 hours to complete the same work. How long will it take to complete if they work together?
One hundred and fifty students are admitted to a school. They are distributed over three sections A, B and C. If 6 students are shifted from section A to section C, the sections will have equal number of students. If 4 times of students of section C exceeds the number of students of section A by the number of students in section B, find the number of students in the three sections
Reduce the given Rational expression to its lowest form
`(x^(3"a") - 8)/(x^(2"a") + 2x^"a" + 4)`
Reduce the given Rational expression to its lowest form
`(10x^3 - 25x^2 + 4x - 10)/(-4 - 10x^2)`
Simplify `(1/("p") + 1/("q" + "r"))/(1/"p" - 1/("q" + "r")) xx [1 + ("q"^2 + "r"^2 - "p"^2)/(2"qr")]`
