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Rational Expressions

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

  1. p(x)/q(x)=(x3-2x)/(8x-4)
  2. p(x)/q(x)=(x3-2x2)/(2x2-4)
  3. p(x)/q(x)=(x2-x+3)/(x-5)
  4. p(x)/q(x)=(x3-2x2-3)/(x2-2)

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). Example
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)