The same thing works for simplifying rational expressions as well but the only difference is of having polynomials in the fraction. In fractions, when the numerator and denominator of a rational number have no common factor other than 1, we consider that it is its simplified form. The simplification of a rational expression is the same as how we simplify fractions. Simplifying rational expressions means reducing the value of a rational expression to its lowest terms or simplified form. Thus, to find the restriction(s) of a rational expression just set the denominator equal to 0 and solve for the variable.
In other words, we say x / (x + 2) takes all values for x but x ≠ -2. For example, in the expression x / (x + 2), the denominator becomes zero when x = -2 and hence it is known as the restriction of the rational expression x / (x + 2). Thus, a rational expression (as it is a fraction) is NOT defined for the value(s) of the variable for which the denominator is equal to 0. Check what is 1/0 using your calculator, it will throw an error. Note that if one of the numerator and denominator is NOT a polynomial, then the fraction is NOT called as a rational expression.ĭividing a number by 0 is not possible. Here are some examples of rational expressions: (x + 1) / (x 2 - 5), (x 3 + 3x 2 - 5) / (4x - 2), etc. Since rational expressions are nothing but fractions, we operate on them just the way we operate the fractions. i.e., it is of the form p(x)/q(x), where q(x) ≠ 0 and p(x) and q(x) are polynomials. In a rational expression, both numerator and denominator are polynomials. Rational expressions are fractions with variables.