Advertisements
Advertisements
Question
If A = `(2x + 1)/(2x - 1)`, B = `(2x - 1)/(2x + 1)` find `1/("A" - "B") - (2"B")/("A"^2 - "B"^2)`
Advertisements
Solution
`1/("A" - "B") - (2"B")/("A"^2 - "B"^2) = 1/("A" - "B") - (2"B")/(("A" + "B")("A" - "B"))`
= `("A" + "B" - 2"B")/(("A" + "B")("A" - "B"))`
= `("A" - "B")/(("A" + "B")("A" - "B"))`
= `1/("A" + "B")`
= `1 ÷ (2x + 1)/(2x - 1) + (2x - 1)/(2x + 1)`
= `1 ÷ ((2x + 1)^2 + (2x - 1)^2)/((2x - 1)(2x + 1))`
= `1 ÷ (4x^2 + 1 + 4x + 4x^2 + 1 - 4x)/((2x - 1)(2x + 1))`
= `1 ÷ (8x^2 + 2)/((2x - 1)(2x + 1))`
= `1 ÷ (2(4x^2 + 1))/(4x^2 - 1)`
= `1 xx (4x^2 - 1)/(2(4x^2 + 1))`
APPEARS IN
RELATED QUESTIONS
Reduce the following rational expression to its lowest form
`(9x^2 + 81x)/(x^3 + 8x^2 - 9x)`
Simplify `(x^3 - y^3)/(3x^2 + 9xy + 6y^2) xx (x^2 + 2xy + y^2)/(x^2 - y^2)`
Simplify `(x + 2)/(4"y") ÷ (x^2 - x - 6)/(12y^2)`
Simplify `(12"t"^2 - 22"t" + 8)/(3"t") ÷ (3"t"^2 + 2"t" - 8)/(2"t"^2 + 4"t")`
Simplify `(x^3)/(x - y) + (y^3)/(y - x)`
Identify rational expression should be subtracted from `(x^2 + 6x + 8)/(x^3 + 8)` to get `3/(x^2 - 2x + 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")]`
Is it possible to design a rectangular park of perimeter 320 m and area 4800 m2? If so find its length and breadth.
At t minutes past 2 pm, the time needed to 3 pm is 3 minutes less than `("t"^2)/4`. Find t.
