Adding and subtracting radicals by combining th Multiplying and dividing radicals by the product rule and quotient rule Rationalizing denominators
In order to remove the radical in the denominators, we use the fact that we can multiply the numerator and the denominator of a fraction by the same nonzero number without changing the value of the expression. Optional: The substitution method in solving equations containing rational expressions
For some equations containing rational expressions, the parts of the expression can be substituted by new variables. After substitutions all the original variables are replaced by new variables, and the algebraic expressions are much simpler and easier to be solved. For example: Dear all, in this class we leaned the multiplication/division and additions/subtraction of rational expressions. The method is just like the calculations of fractional numbers that you leaned before (fractional numbers are also rational expressions, right?). Please keep in mind that you need to factor the denominators completely to find the LCD (for addition/substration), and to factor the numerators completely as well to simplify the rational expressions.
Here are some key points and examples: Today we expand our knowledge of algebraic expressions to include another category called rational expressions. Please note that a fractional number is also a rational expression, thus all the methods you learned before for the calculations of fractions can be expanded to algebraic expressions. A rational expression is undefined for values that make the denominator 0.
Cross product is a good method for factoring polynomials. Please make sure to understand how to use it. Here is one video for the method. Remember before factoring a trinomial you must determine if there is a greatest common factor (GCF) or not. If there is a GCF, factor that out and then start factoring with criss cross.
https://www.youtube.com/watch?v=nz058Hil6rA Factoring is the reverse process of multiplying. The first step in factoring a polynomial is to see whether the terms of the polynomial have a common factor. If there is one, we can write the polynomial as a product by factoring out the common factor. We will usually factor out the greatest common factor (GCF). The GCF of a list of variables is the variable raised to the smallest exponent in the list.
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October 2016
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