Advertisements
Advertisements
Question
Identify rational expression should be subtracted from `(x^2 + 6x + 8)/(x^3 + 8)` to get `3/(x^2 - 2x + 4)`
Advertisements
Solution
Let p(x) = `(x^2 + 6x + 8)/(x^3 + 8)`
p(x) − q(x) = `3/(x^2 - 2x + 4)`
`(x^2 + 6x + 8)/(x^3 + 8) - "q"(x) = 3/(x^2 - 2x + 4)`
q(x) = `(x^2 + 6x + 8)/(x^3 + 8) - 3/(x^2 - 2x + 4)`
q(x) = `(x^2 + 6x + 8)/((x + 2)(x^2 - 2x + 4)) - 3/(x^2 - 2x + 4)`
= `((x + 2)(x + 4))/((x + 2)(x^2 - 2x + 4)) - 3/(x^2 - 2x + 4)`
= `(x + 4)/(x^2 - 2x + 4) - 3/(x^2 - 2x + 4)`
= `(x + 4 - 3)/(x^2 - 2x + 4)`
= `(x + 1)/(x^2-2x+4)`
APPEARS IN
RELATED QUESTIONS
Reduce the following rational expression to its lowest form
`(x^2 - 11x + 18)/(x^2 - 4x + 4)`
Find the excluded values, of the following expression
`(x^3 - 27)/(x^3 + x^2 - 6x)`
Simplify `(4x^2y)/(2z^2) xx (6xz^3)/(20y^4)`
Simplify `(x + 4)/(3x + 4y) xx (9x^2 - 16y^2)/(2x^2 + 3x - 20)`
If x = `("a"^2 + 3"a" - 4)/(3"a"^2 - 3)` and y = `("a"^2 + 2"a" - 8)/(2"a"^2 - 2"a" - 4)` find the value of x2y–2
Simplify `(x(x + 1))/(x - 2) + (x(1 - x))/(x - 2)`
Simplify `(4x)/(x^2 - 1) - (x + 1)/(x - 1)`
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)`
Arul, Madan and Ram working together can clean a store in 6 hours. Working alone, Madan takes twice as long to clean the store as Arul does. Ram needs three times as long as Arul does. How long would it take each if they are working alone?
