Search for tag: "bottom"

Solving a rational equation that simplifies to quadratic: Proportional form, advanced

This shows how to use the LCD of the two fractions that form a proportion to simplify the equation to a quadratic equation, then solve the quadratic by factoring and check the validity of the …

From  Tom Grant 10 plays 0  

Solving rational equations that simplify to quadratic: Binomial denominators & numerators

A The key to solving this kind of equation is multiplying through by the least common denominator to eliminate the fractions first, Then it is a matter of combining like terms on one side of the…

From  Tom Grant 55 plays 0  

Rationalizing a denominator: Quotient involving square roots

This shows how to multiply by a form of one created by using the irrational denominaor to multiply by the top and the bottom of the fraction creating a whole number denominaor.

From  Tom Grant 9 plays 0  

Rational exponents: Quotient Rule

Demonstrates how the quotient rule for exponents is applied the same way to rational exponents.

From  Tom Grant 14 plays 0  

Adding rational expressions with linear denominators without common factors: Basic

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…

From  Tom Grant 9 plays 0  

Complex fraction with negative exponents: Problem type 2

This demonstrates how to transform variables with negative exponents into corresponding reciprocal fractions, and then proceed to simplify the resulting complex fraction by multiplying all terms by…

From  Tom Grant 11 plays 0  

Complex fraction made of sums involving rational expressions: Multivariate

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.

From  Tom Grant 14 plays 0  

Complex fraction made of sums involving rational expressions: Problem type 3

A complex fraction is multiplied through on the top and the bottom by the common denominator of all smaller fractions, eliminating the denominators of those smaller fractions.

From  Tom Grant 11 plays 0  

Complex fraction made of sums involving rational expressions: Problem type 1

Simplifies a complex fraction by multiplying the top and bottom by the common denominator of the smaller fractions so their denominators can be eliminated. Further simplification is considered.

From  Tom Grant 19 plays 0  

Adding rational expressions involving different quadratic denominators

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…

From  Tom Grant 6 plays 0  

Adding rational expressions with linear denominators with common factors: Basic

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…

From  Tom Grant 22 plays 0  

Adding rational expressions with multivariate monomial denominators: Basic

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…

From  Tom Grant 6 plays 0  

Adding rational expressions with common denominators & GCF factoring

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. …

From  Tom Grant 6 plays 0  

Adding rational expressions with common denominators and binomial numerators

This demonstrates adding two rational expressions that have different terms individually in the numerator and a common denominator. When the fractions are added, it creates the possibility of adding…

From  Tom Grant 9 plays 0  

Dividing rational expressions involving linear expressions

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…

From  Tom Grant 6 plays 0  

Dividing rational expressions involving multivariate monomials

A quick justification of dividing fractions by multiplying by the reciprocal of the second fraction in the division followed by an example that involves reducing the common factors in the numerator…

From  Tom Grant 5 plays 0