if(ax2+bx+c)y+a'x2+b'x+c'=0.........find the condition that x may be a rational functional of y......

Rational function is defined in similar fashion as rational number is defined in terms of numerator and denominator. Implicitly, we refer “real” rational function here. It is defined as the ratio of two real polynomials with the condition that polynomial in the denominator is not a zero polynomial.

                                    f(x) = p(x)/q(x) for q(x) not equal to 0

Rational function is not defined for values of x for which denominator polynomial evaluates to zero as ratio “p(x)/0” is not defined

here y = -(a'x²+b'x+c)/(ax²+bx+c) is rational if

ax²+bx+c not equal to 0

implies x not equal to -b/2a + (b²-4ac)^1/2 / 2a   and  -b/2a - (b²-4ac)^1/2 / 2a

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regards

Ramesh