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A simple fraction (also known as a common fraction or vulgar fraction, where vulgar is Latin for "common") is a rational number written as a/b or , where a and b are both integers. [9] As with other fractions, the denominator (b) cannot be zero. Examples include 1 / 2 , − 8 / 5 , −8 / 5 , and 8 / −5
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. [1]
If n is a negative integer, is defined only if x has a multiplicative inverse. [35] In this case, the inverse of x is denoted x −1, and x n is defined as (). Exponentiation with integer exponents obeys the following laws, for x and y in the algebraic structure, and m and n integers:
An irreducible fraction (or fraction in lowest terms, simplest form or reduced fraction) is a fraction in which the numerator and denominator are integers that have no other common divisors than 1 (and −1, when negative numbers are considered). [1]
This helps to simplify mathematical computations by reducing the number of basic arithmetic operations needed to perform calculations. [48] The additive identity element is 0 and the additive inverse of a number is the negative of that number. For instance, + = and + =. Addition is both commutative and associative.
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Simplifying this further gives us the solution x = −3. It is easily checked that none of the zeros of x ( x + 1)( x + 2) – namely x = 0 , x = −1 , and x = −2 – is a solution of the final equation, so no spurious solutions were introduced.