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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.
It is also used for fractions within fractions (complex fractions) or within exponents to increase legibility. Fractions written this way, also known as piece fractions, [31] are written all on one typographical line, but take 3 or more typographical spaces. Built-up fractions: . This notation uses two or more lines of ordinary text and results ...
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.
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 denominator is 1. An expression which is not in fractional form is an integral expression. An integral expression can always be written in fractional form by giving it the denominator 1.
Shop staff were robbed at knifepoint during a "terrifying incident" that resulted in £80 being stolen, police have said. A man in his 20s has been arrested on suspicion of robbery in connection ...
This is a common procedure in mathematics, used to reduce fractions or calculate a value for a given variable in a fraction. If we have an equation =, where x is a variable we are interested in solving for, we can use cross-multiplication to determine that =.