Advertisements
Advertisements
प्रश्न
If A = `x/(x + 1)` B = `1/(x + 1)` prove that `(("A" + "B")^2 + ("A" - "B")^2)/("A" + "B") = (2(x^2 + 1))/(x(x + 1)^2`
Advertisements
उत्तर
(A + B)2 = `(x/(x + 1) + 1/(x + 1))^2`
= `((x + 1)/(x + 1))^2`
= 1
(A – B)2 = `(x/(x + 1) - 1/(x + 1))^2`
= `((x - 1)/(x + 1))^2`
= `(x - 1)^2/(x + 1)^2`
`"A"/"B" = x/(x + 1) ÷ 1/(x + 1)`
= `x/(x + 1) xx (x + 1)/1`
= x
L.H.S. = `(("A" + "B")^2 + ("A" - "B")^2)/("A"/"B")`
= `1 + (x - 1)^2/(x + 1)^2 ÷ x`
= `((x + 1)^2 + (x - 1)^2)/(x + 1)^2 xx 1/x`
= `(x^2 + 2x + 1 + x^2 - 2x + 1)/(x(x + 1)^2`
= `(2x^2 + 2)/(x(x + 1)^2`
= `(2(x^2 + 1))/(x(x + 1)^2`
L.H.S. = R.H.S.
APPEARS IN
संबंधित प्रश्न
Reduce the following rational expression to its lowest form
`(x^2 - 1)/(x^2 + x)`
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
`(x^2 + 6x + 8)/(x^2 + x - 2)`
Find the excluded values, of the following expression
`(x^3 - 27)/(x^3 + x^2 - 6x)`
Simplify `(2"a"^2 + 5"a" + 3)/(2"a"^2 + 7"a" + 6) ÷ ("a"^2 + 6"a" + 5)/(-5"a"^2 - 35"a" - 50)`
If A = `(2x + 1)/(2x - 1)`, B = `(2x - 1)/(2x + 1)` find `1/("A" - "B") - (2"B")/("A"^2 - "B"^2)`
Solve `1/3` (x + y – 5) = y – z = 2x – 11 = 9 – (x + 2z)
Reduce the given Rational expression to its lowest form
`(x^(3"a") - 8)/(x^(2"a") + 2x^"a" + 4)`
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.
