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((3*x^2-y^2+36*x+107)*(x^2-y^2+5*x+6)-(2*x+5)*(x^3-3*x*y^2+18*x^2-18*y^2+107*x+210))/((x^2-y^2+5*x+6)^2+4*x^2*y^2+25*y^2+20*x*y^2)=0

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((3*x^2-y^2+36*x+107)*(x^2-y^2+5*x+6)-(2*x+5)*(x^3-3*x*y^2+18*x^2-18*y^2+107*x+210))/((x^2-y^2+5*x+6)^2+4*x^2*y^2+25*y^2+20*x*y^2)=0

What you mean?

(-(2*x + 5)*(x^3 + 18*x^2 - 3*x*y^2 + 107*x - 18*y^2 + 210) + (x^2 + 5*x - y^2 + 6)*(3*x^2 + 36*x - y^2 + 107))/(4*x^2*y^2 + 20*x*y^2 + 25*y^2 + (x^2 + 5*x - y^2 + 6)^2) = 0
 
(-(2*x + 5)*(x^3 + 18*x^2 - 3*x*y^2 + 107*x - 18*y^2 + 210) + (x^2 + 5*x - y^2 + 6)*(3*x^2 + 36*x - y^2 + 107))/(20*x*y^2 + 4*x^((2*y)^2) + 25*y^2 + (x^2 + 5*x - y^2 + 6)^2) = 0
 
(-(2*x + 5)*(x^3 + 18*x^2 - 3*x*y^2 + 107*x - 18*y^2 + 210) + (x^2 + 5*x - y^2 + 6)*(3*x^2 + 36*x - y^2 + 107))/(20*x*y^2 + 4*x^((2*y)^2) + 25*y^2 + (x^2 + 5*x - y^2 + 6)^2) = 0

Plot ((3*x^2-y^2+36*x+107)*(x^2-y^2+5*x+6)-(2*x+5)*(x^3-3*x*y^2+18*x^2-18*y^2+107*x+210))/((x^2-y^2+5*x+6)^2+4*x^2*y^2+25*y^2+20*x*y^2)=0

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The solution

You have entered [src] 
/   2    2             \ / 2    2          \             / 3        2       2       2              \    
\3*x  - y  + 36*x + 107/*\x  - y  + 5*x + 6/ - (2*x + 5)*\x  - 3*x*y  + 18*x  - 18*y  + 107*x + 210/    
---------------------------------------------------------------------------------------------------- = 0
                                             2                                                          
                          / 2    2          \       2  2       2         2                              
                          \x  - y  + 5*x + 6/  + 4*x *y  + 25*y  + 20*x*y
$$\frac{- \left(2 x + 5\right) \left(\left(107 x + \left(- 18 y^{2} + \left(18 x^{2} + \left(x^{3} - 3 x y^{2}\right)\right)\right)\right) + 210\right) + \left(\left(5 x + \left(x^{2} - y^{2}\right)\right) + 6\right) \left(\left(36 x + \left(3 x^{2} - y^{2}\right)\right) + 107\right)}{20 x y^{2} + \left(25 y^{2} + \left(4 x^{2} y^{2} + \left(\left(5 x + \left(x^{2} - y^{2}\right)\right) + 6\right)^{2}\right)\right)} = 0$$
Find derivative
The graph of the function
The graph
Plot ((3*x^2-y^2+36*x+107)*(x^2-y^2+5*x+6)-(2*x+5)*(x^3-3*x*y^2+18*x^2-18*y^2+107*x+210))/((x^2-y^2+5*x+6)^2+4*x^2*y^2+25*y^2+20*x*y^2)=0

    Examples of implicit functions

    Learn more about Implicit function

    The above examples also contain:

    • the modulus or absolute value: absolute(x) or |x|
    • square roots sqrt(x),
      cubic roots cbrt(x)
    • trigonometric functions:
      sinus sin(x), cosine cos(x), tangent tan(x), cotangent ctan(x)
    • exponential functions and exponents exp(x)
    • inverse trigonometric functions:
      arcsine asin(x), arccosine acos(x), arctangent atan(x), arccotangent acot(x)
    • natural logarithms ln(x),
      decimal logarithms log(x)
    • hyperbolic functions:
      hyperbolic sine sh(x), hyperbolic cosine ch(x), hyperbolic tangent and cotangent tanh(x), ctanh(x)
    • inverse hyperbolic functions:
      hyperbolic arcsine asinh(x), hyperbolic arccosinus acosh(x), hyperbolic arctangent atanh(x), hyperbolic arccotangent acoth(x)
    • other trigonometry and hyperbolic functions:
      secant sec(x), cosecant csc(x), arcsecant asec(x), arccosecant acsc(x), hyperbolic secant sech(x), hyperbolic cosecant csch(x), hyperbolic arcsecant asech(x), hyperbolic arccosecant acsch(x)
    • rounding functions:
      round down floor(x), round up ceiling(x)
    • the sign of a number:
      sign(x)
    • for probability theory:
      the error function erf(x) (integral of probability), Laplace function laplace(x)
    • Factorial of x:
      x! or factorial(x)
    • Gamma function gamma(x)
    • Lambert's function LambertW(x)
    • Trigonometric integrals: Si(x), Ci(x), Shi(x), Chi(x)

    The insertion rules

    The following operations can be performed

    2*x
    - multiplication
    3/x
    - division
    x^2
    - squaring
    x^3
    - cubing
    x^5
    - raising to the power
    x + 7
    - addition
    x - 6
    - subtraction
    Real numbers
    insert as 7.5, no 7,5

    Constants

    pi
    - number Pi
    e
    - the base of natural logarithm
    i
    - complex number
    oo
    - symbol of infinity
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