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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 .
An idiom is an expression that has a figurative meaning often related, but different from the literal meaning of the phrase. Example: You should keep your eye out for him. A pun is an expression intended for a humorous or rhetorical effect by exploiting different meanings of words. Example: I wondered why the ball was getting bigger. Then it ...
Metalepsis: figurative speech is used in a new context. Metaphor: an implied comparison between two things, attributing the properties of one thing to another that it does not literally possess. [19] Metonymy: a thing or concept is called not by its own name but rather by the name of something associated in meaning with that thing or concept.
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
Analysts group metaphors with other types of figurative language, such as antithesis, hyperbole, metonymy, and simile. [3] “ Figurative language examples include “similes, metaphors, personification, hyperbole, allusions, and idioms.”” [ 4 ] One of the most commonly cited examples of a metaphor in English literature comes from the " All ...
In complex analysis, a partial fraction expansion is a way of writing a meromorphic function as an infinite sum of rational functions and polynomials. When f ( z ) {\displaystyle f(z)} is a rational function, this reduces to the usual method of partial fractions .
Expressions can be evaluated or simplified by replacing operations that appear in them with their result, or by combining like-terms. [ 21 ] For example, take the expression 4 x 2 + 8 {\displaystyle 4x^{2}+8} ; it can be evaluated at x = 3 in the following steps:
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.