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
`("p"^2 - 3"p" - 40)/(2"p"^3 - 24"p"^2 + 64"p")`
Simplify `(4x^2y)/(2z^2) xx (6xz^3)/(20y^4)`
Simplify `(5"t"^3)/(4"t" - 8) xx (6"t" - 12)/(10"t")`
Simplify `(x + 4)/(3x + 4y) xx (9x^2 - 16y^2)/(2x^2 + 3x - 20)`
Simplify `(2"a"^2 + 5"a" + 3)/(2"a"^2 + 7"a" + 6) ÷ ("a"^2 + 6"a" + 5)/(-5"a"^2 - 35"a" - 50)`
Simplify `(x^3)/(x - y) + (y^3)/(y - x)`
Simplify `((2x + 1)(x - 2))/(x - 4) - ((2x^2 - 5x + 2))/(x - 4)`
Simplify `(4x)/(x^2 - 1) - (x + 1)/(x - 1)`
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?
At t minutes past 2 pm, the time needed to 3 pm is 3 minutes less than `("t"^2)/4`. Find t.
