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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]
A simple fraction (also known as a common fraction or vulgar fraction) [n 1] 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 .
If the discriminant is zero the fraction converges to the single root of multiplicity two. If the discriminant is positive the equation has two real roots, and the continued fraction converges to the larger (in absolute value) of these. The rate of convergence depends on the absolute value of the ratio between the two roots: the farther that ...
PDF Solutions, Inc. is an American multinational software and engineering services company based in Santa Clara, California. The company is listed in the Nasdaq stock exchange under the ticker symbol PDFS.
The fifth person to be elected president while losing the popular vote, [c] he received nearly 2.9 million fewer votes than Clinton, 46.3% to her 48.25%. [138] He was the only president who neither served in the military nor held any government office prior to becoming president. [ 139 ]
The fractional distillation of organic substances played an important role in the 9th-century works attributed to the Islamic alchemist Jabir ibn Hayyan, as for example in the Kitāb al-Sabʿīn ('The Book of Seventy'), translated into Latin by Gerard of Cremona (c. 1114–1187) under the title Liber de septuaginta. [1]
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