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Simplify- (x-y)/(xy)+(y-z)/(yz)+(z-x...

Simplify-
`(x-y)/(xy)+(y-z)/(yz)+(z-x)/(zx)`

Answer

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If xy + yz + zx = 1 find (x+y)/(1-xy) + (y+z)/(1-yz) + (z + x)/(1-zx) = ?

simplify- (((x+y)^2-xy)/((y-z)(z-x)))+(((y+z)^2-yz)/((z-x)(x-y)))+(((z+x)^2-zx)/((x-y)(y-z)))

Knowledge Check

  • If x^(3)+y^(3)+z^(3)=3xyz and x+y+z=0 , then the value of ((x+y)^(2))/(xy)+((y+z)^(2))/(yz)+((z+x)^(2))/(zx) is

    A
    xyz
    B
    `3`
    C
    `3` xyz
    D
    `1`

  • If x + y + z = 0 , then the value of (x^2)/(yz) + (y^2)/(zx) + (z^2)/(xy) is:

    A
    3
    B
    `-3`
    C
    `0`
    D
    `3xyz`

  • If x + y + z = 22 and xy + yz + zx = 35 , then what is the value of ( - y)^(2) + ( y - z)^(2) + ( z - x)^(2) ?

    A
    793
    B
    681
    C
    758
    D
    715

    • Similar Questions

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    If x^(3)+y^(3)+z^(3)=3xyz and x+y+z=0, find the value of ((x+y)^(2))/(xy)=((y+z)^(2))/(yz) +((z+x)^(2))/(zx)

    Simplify- (x-y-z)(x^2+y^2+z^2+xy-yz+zx)

    Prove that |{:(x^(2),,x^(2)-(y-z)^(2),,yz),(y^(2),,y^(2)-(z-x)^(2),,zx),(z^(2),,z^(2)-(x-y)^(2),,xy):}| =(x-y) (y-z) (z-x)(x+y+z) (x^(2)+y^(2)+z^(2))

    If (x^(2)-yz)/(a) =(y^(2)-zx)/(b) =(z^(2)-xy)/(c ) , then (x+y+z) (a+b+c) =ax +by +cz

    If (xy log(xy))/(x+y) = (yz (log (yz))/(y+z)) = (zx(log (zx))/(z+x)) , then show that x^(x) = y^(y) =z^(x)

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