Rational expressions is defined as the quotient p(x)/q(x) of two polynomials p(x) and q(x) where q(x) is non zero polynomial.
for example if p(x)=x2-2x and q(x)=2x-4 (non zero polynomial) are two polynomials then quotient p(x)/q(x)=x2-2x/2x-4 is known as rational expression of polynomials.where p(x) is known as numerator and q(x) is known as denominator of rational expression.
Example of rational expression
Equality of rational expressions
Two Rational expressions are always equal if numerator of 1st expression * denominator of 2nd expression is equal to denominator of 1st expression * numerator of 2nd expression.
For example if you have two rational expression p(x)/q(x) and m(x)/n(x) then that rational expression are said to be equal if p(x)n(x)=q(x)m(x).
Addition of rational expressions
Sum of two rational expressions is defined as (p(x)n(x)+m(x)q(x))/(n(x)q(x)) where rational expressions of polynomials are p(x)/q(x) and m(x)/n(x).
first rational expressions is x+4/x-8 and second rational expressions is x2+3/x-1 then addition of rational expressions are
Sum of two rational expressions is ((x+4)*(x-1)+ (x2+3)*(x-8))/(x-8)(x-1)