Ads
related to: simplifying fractions with exponents algebra
Search results
Results From The WOW.Com Content Network
In algebra, the partial fraction decomposition or partial fraction expansion of a rational fraction (that is, a fraction such that the numerator and the denominator are both polynomials) is an operation that consists of expressing the fraction as a sum of a polynomial (possibly zero) and one or several fractions with a simpler denominator.
For example, the numerators of fractions with common denominators can simply be added, such that + = and that <, since each fraction has the common denominator 12. Without computing a common denominator, it is not obvious as to what 5 12 + 11 18 {\displaystyle {\frac {5}{12}}+{\frac {11}{18}}} equals, or whether 5 12 {\displaystyle {\frac {5 ...
A field is an algebraic structure in which multiplication, addition, subtraction, and division are defined and satisfy the properties that multiplication is associative and every nonzero element has a multiplicative inverse. This implies that exponentiation with integer exponents is well-defined, except for nonpositive powers of 0.
The terminology used to describe algebraic fractions is similar to that used for ordinary fractions. For example, an algebraic fraction is in lowest terms if the only factors common to the numerator and the denominator are 1 and −1. An algebraic fraction whose numerator or denominator, or both, contain a fraction, such as + , is called ...
The result is an equation with no fractions. The simplified equation is not entirely equivalent to the original. For when we substitute y = 0 and z = 0 in the last equation, both sides simplify to 0, so we get 0 = 0, a mathematical truth.
The numerator and denominator are called the terms of the algebraic fraction. A complex fraction is a fraction whose numerator or denominator, or both, contains a fraction. A simple fraction contains no fraction either in its numerator or its denominator. A fraction is in lowest terms if the only factor common to the numerator and the ...
Simplification of algebraic expressions, in computer algebra; Simplification of boolean expressions i.e. logic optimization; Simplification by conjunction elimination in inference in logic yields a simpler, but generally non-equivalent formula; Simplification of fractions
In calculus and mathematical analysis, algebraic operation is also used for the operations that may be defined by purely algebraic methods. For example, exponentiation with an integer or rational exponent is an algebraic operation, but not the general exponentiation with a real or complex exponent. Also, the derivative is an operation that is ...