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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. But the same substitution applied to the original equation results in x/6 + 0/0 = 1, which is mathematically meaningless.
A rational algebraic expression (or rational expression) is an algebraic expression that can be written as a quotient of polynomials, such as x 2 + 4x + 4. An irrational algebraic expression is one that is not rational, such as √ x + 4.
If the expressions a and b are polynomials, the algebraic fraction is called a rational algebraic fraction [1] or simply rational fraction. [2] [3] Rational fractions are also known as rational expressions.
If the numerator and the denominator are polynomials, as in + , the algebraic fraction is called a rational fraction (or rational expression). An irrational fraction is one that is not rational, as, for example, one that contains the variable under a fractional exponent or root, as in x + 2 x 2 − 3 {\displaystyle {\frac {\sqrt {x+2 ...
Simplification is the process of replacing a mathematical expression by an equivalent one that is simpler (usually shorter), according to a well-founded ordering. Examples include: Simplification of algebraic expressions, in computer algebra; Simplification of boolean expressions i.e. logic optimization
A formal expression is a kind of string of symbols, created by the same production rules as standard expressions, however, they are used without regard to the meaning of the expression. In this way, two formal expressions are considered equal only if they are syntactically equal, that is, if they are the exact same expression.
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A complex rational function with degree one is a Möbius transformation. Rational functions are representative examples of meromorphic functions. [3] Iteration of rational functions on the Riemann sphere (i.e. a rational mapping) creates discrete dynamical systems. [4] Julia sets for rational maps