Lesson OVERVIEW of lessons on simplifying and rationalizing expressions and functions (denominators)

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OVERVIEW of lessons on simplifying and rationalizing expressions and functions (denominators)


This file is an OVERVIEW of my lessons on simplifying and rationalizing expressions and functions (denominators).
For your convenience,  it contains the list of the lessons and then the same list with short annotations to each lesson.
    - HOW TO rationalize a fraction by making its denominator free of square roots
    - HOW TO rationalize a fraction by making its denominator free of cubic roots
    - Amazing calculations with fractions that contain quadratic irrationalities in denominators

List of lessons with short annotations

HOW TO rationalize a fraction by making its denominator free of square roots

     Example 1.  Transform the fraction 1%2F%28sqrt%282%29-1%29 to make it free of the square root in the denominator.

     Example 2.  Transform the fraction %28sqrt%283%29%2B1%29%2F%28sqrt%283%29-1%29 to make it free of the square root in the denominator.

     Example 3.  Rationalize the fraction sqrt%285%29%2F%28sqrt%285%29%2B1%29.

     Example 4.  If   x = %282%2Bsqrt%283%29%29%2F%282-sqrt%283%29%29,   then find the value of   x+%2B+1%2Fx.


HOW TO rationalize a fraction by making its denominator free of cubic roots

     Example 1.  Transform the fraction   1%2F%28root%283%2C2%29-1%29   to make it free of the cubic root in the denominator.

     Example 2.  Transform the fraction   1%2F%28root%283%2C2%29%2B1%29   to make it free of the cubic root in the denominator.

     Example 3.  Simplify the expression   1%2F%28root%283%2Ca%5E2%29+-+root%283%2Ca%29+%2B+1%29   +   1%2F%28root%283%2Ca%29+%2B+1%29.

Amazing calculations with fractions that contain quadratic irrationalities in denominators

     Problem 1.  Simplify the fraction  1%2F%28sqrt%282%29+%2B+1%29.

     Problem 2.  Simplify and find the value of the sum of fractions  1%2F%28sqrt%282%29+%2B+1%29 + 1%2F%28sqrt%283%29+%2B+sqrt%282%29%29.

     Problem 3.  Simplify and find the value of the sum of fractions  1%2F%28sqrt%282%29+%2B+1%29 + 1%2F%28sqrt%283%29+%2B+sqrt%282%29%29 + 1%2F%28sqrt%284%29+%2B+sqrt%283%29%29.

     Problem 4.  Simplify the sum of fractions  1%2F%28sqrt%282%29+%2B+1%29 + 1%2F%28sqrt%283%29+%2B+sqrt%282%29%29 + 1%2F%28sqrt%284%29+%2B+sqrt%283%29%29 + . . . + 1%2F%28sqrt%28n%29+%2B+sqrt%28n-1%29%29.

     Problem 5.  Simplify the fraction  1%2F%28sqrt%283%29+%2B+1%29.

     Problem 6.  Simplify and find the value of the sum of fractions  1%2F%28sqrt%283%29+%2B+1%29 + 1%2F%28sqrt%285%29+%2B+sqrt%283%29%29.

     Problem 7.  Simplify and find the value of the sum of fractions  1%2F%28sqrt%283%29+%2B+1%29 + 1%2F%28sqrt%285%29+%2B+sqrt%283%29%29 + 1%2F%28sqrt%287%29+%2B+sqrt%285%29%29.

     Problem 8.  Simplify the sum of fractions  1%2F%28sqrt%283%29+%2B+1%29 + 1%2F%28sqrt%285%29+%2B+sqrt%283%29%29 + 1%2F%28sqrt%287%29+%2B+sqrt%285%29%29 + . . . + 1%2F%28sqrt%282n%2B1%29+%2B+sqrt%282n-1%29%29.

     Problem 9.  Simplify the sum of fractions  1%2F%28sqrt%284%29+%2B+1%29 + 1%2F%28sqrt%287%29+%2B+sqrt%284%29%29 + 1%2F%28sqrt%2810%29+%2B+sqrt%287%29%29 + . . . + 1%2F%28sqrt%283n%2B1%29+%2B+sqrt%283%28n-1%29%2B1%29%29.


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