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For example, a fraction is put in lowest terms by cancelling out the common factors of the numerator and the denominator. [2] As another example, if a×b=a×c, then the multiplicative term a can be canceled out if a≠0, resulting in the equivalent expression b=c; this is equivalent to dividing through by a.
In elementary algebra, root rationalisation (or rationalization) is a process by which radicals in the denominator of an algebraic fraction are eliminated.. If the denominator is a monomial in some radical, say , with k < n, rationalisation consists of multiplying the numerator and the denominator by , and replacing by x (this is allowed, as, by definition, a n th root of x is a number that ...
English: A diagram demonstrating endodontic therapy (colloquially known as a root canal) on unhealthy or injured tooth: first drilling and cleaning, then filing with an endofile, and finally adding the rubber filling and crown.
Doubling the cube is the construction, using only a straightedge and compass, of the edge of a cube that has twice the volume of a cube with a given edge. This is impossible because the cube root of 2, though algebraic, cannot be computed from integers by addition, subtraction, multiplication, division, and taking square roots.
The surprising part of the character formula is that when we compute this product, only a small number of terms actually remain. Many more terms than this occur at least once in the product of the character and the Weyl denominator, but most of these terms cancel out to zero. [5]
Specifically, it is the subgroup which is generated by reflections through the hyperplanes orthogonal to at least one of the roots, and as such is a finite reflection group. In fact it turns out that most finite reflection groups are Weyl groups. [1] Abstractly, Weyl groups are finite Coxeter groups, and are important examples of these.
The first step is to determine a common denominator D of these fractions – preferably the least common denominator, which is the least common multiple of the Q i. This means that each Q i is a factor of D, so D = R i Q i for some expression R i that is not a fraction. Then
An unusual root canal shape, complex branching (especially the existence of horizontal branches), and multiple root canals are considered as the main causes of root canal treatment failures. (e.g. If a secondary root canal goes unnoticed by the dentist and is not cleaned and sealed, it will remain infected, causing the root canal therapy to fail).