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  2. Equating coefficients - Wikipedia

    en.wikipedia.org/wiki/Equating_coefficients

    A similar problem, involving equating like terms rather than coefficients of like terms, arises if we wish to de-nest the nested radicals + to obtain an equivalent expression not involving a square root of an expression itself involving a square root, we can postulate the existence of rational parameters d, e such that

  3. Fraction - Wikipedia

    en.wikipedia.org/wiki/Fraction

    The process for subtracting fractions is, in essence, the same as that of adding them: find a common denominator, and change each fraction to an equivalent fraction with the chosen common denominator. The resulting fraction will have that denominator, and its numerator will be the result of subtracting the numerators of the original fractions.

  4. Equality (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Equality_(mathematics)

    In mathematics, equality is a relationship between two quantities or expressions, stating that they have the same value, or represent the same mathematical object. [1] Equality between A and B is written A = B, and pronounced "A equals B". In this equality, A and B are distinguished by calling them left-hand side (LHS), and right-hand side (RHS).

  5. Irreducible fraction - Wikipedia

    en.wikipedia.org/wiki/Irreducible_fraction

    An equivalent definition is sometimes useful: if a and b are integers, then the fraction ⁠ a / b ⁠ is irreducible if and only if there is no other equal fraction ⁠ c / d ⁠ such that | c | < | a | or | d | < | b |, where | a | means the absolute value of a. [4] (Two fractions ⁠ a / b ⁠ and ⁠ c / d ⁠ are equal or equivalent if and ...

  6. Expression (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Expression_(mathematics)

    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.

  7. Equivalence relation - Wikipedia

    en.wikipedia.org/wiki/Equivalence_relation

    Equality is also the only relation on a set that is reflexive, symmetric and antisymmetric. In algebraic expressions, equal variables may be substituted for one another, a facility that is not available for equivalence related variables. The equivalence classes of an equivalence relation can substitute for one another, but not individuals ...

  8. Clearing denominators - Wikipedia

    en.wikipedia.org/wiki/Clearing_denominators

    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 .

  9. Indeterminate form - Wikipedia

    en.wikipedia.org/wiki/Indeterminate_form

    Indeterminate form is a mathematical expression that can obtain any value depending on circumstances. In calculus, it is usually possible to compute the limit of the sum, difference, product, quotient or power of two functions by taking the corresponding combination of the separate limits of each respective function.

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