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Two examples of distributing radicals into a sum of other radicals and simplifying in the process.
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Just a quick couple of examples, one explaining the relationship between squaring and square rooting and one that just shows how to multiply two radical expressions that need no reduction.
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Two examples are shown here, one relatively easy, then one with some fractions involved.
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The key to solving this equation is eliminating the fractions first by multiplying by the least common denominator and dividingout equal factors. Note that the integer term must be multiplied by…
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Describes how to approach solving a radical eqaution, then demonstrates the stepss needed. It finishes with a check of the answers, stressing that this is an essential step.
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A simple demonstration of how the product rule forexponents still applies when the exponents are fractions
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A subtraction of fractionso where the denominators have no factors in common so we simpllly multiply the two together to create the LCD. Then both fractions are adjusted by multiplying each…
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Simplifies a complex fraction by distributing the LCD of each small fraction across the top and the bottom so that all small fractions can be swept away.
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Adding ratioinal expressions with quadratic denominators requires factoring each denominator so that the LCD can be determined. Then each fraction is exapanded by multiplying the tops and the…
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This shows how to determine a common denominator when the denominators share at least one factor. A numerical version is included for more understanding, and the rational expressions are added and…
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This example shows how to factor each denominator and then determine which of these factors are needed to create the least common denominator (LCD). Then the fractions are expanded by multiplying…
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An example that is easy to combine with subtraction, in this case, because the two fractions have common denominators. However, be aware that there may be a way to simplifying the answer further. …
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Each denominator is factored and then any common factor is used only once and all other unique factors complete the LCD
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A demonstration of how factoring is used to discover the minumum number of factors that need to be combined to find the smallest denominator that can be used as the LCD of the two given fractions.
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A brief informal reasoning of why any division can be changed to a multiplication by reciprocating the second number or fraction, i. e. the number going into the other number. Then an example of…
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This is a quick example of factoring the numerator and denominator of a combined fraction where all the factors are separated in order to find those that divide to one.
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