How do rational expressions and rational equations differ?
Difference Between Rational Expressions & Rational Equations
Rational expressions and rational equations are two very different things. [
Their most general difference is that a rational expression is composed of a polynomial numerator and denominator. A rational exponent can be a rational expression or a constant fraction.
A rational expression is a fraction where at
least one term is a polynomial of the form ax² + bx + c, where a, b and c are constant coefficients. In the sciences, rational expressions are used as simplified models of complex equations in order to more easily approximate results without requiring time-consuming complex math. Rational expressions are commonly used to describe phenomena in sound design, photography, aerodynamics, chemistry and physics. Unlike rational exponents, a rational expression is an entire expression, not just a component.
Rational Number Exponents
An expression with a rational exponent is simply a term raised to the power of a fraction. Terms with rational number exponents are equivalent to root expressions with the degree of the denominator of the exponent. For example, the cube root of 3 is equivalent to 3^(1/3). The numerator of the rational exponent is equivalent to the power of the base number when in its radical form. For example, 5^(4/5) is equivalent to the fifth root of 5^4. A negative rational exponent indicates the reciprocal of the radical form. For example, 5^(-4/5) = 1 / 5^(4/5).
There are no new answers.