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Solving a quadratic equation by completing the square: Exact Answers

Two examples are shown here, one relatively easy, then one with some fractions involved.

From  Tom Grant 4 plays 0  

Solving an exponential equation by finding common bases: Linear exponents

Shows how to create common bases so that then the exponents can be set equal to each other and that equation can be solved.

From  Tom Grant 22 plays 0  

Word problem involving the maximum or minimum of a quadratic function

This video explains the situation we are trying to minimize or maximize and the role of the input and output variables. Then the process of finding the location and value of the requested amount is…

From  Tom Grant 11 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 20 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 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 denominators ax and bx: Basic

This example shows how to add fractions with different denominators by adjusting one of the fractions so that they have a common denominator.

From  Tom Grant 7 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  

Finding the LCD of rational expressions with quadratic denominators

Each denominator is factored and then any common factor is used only once and all other unique factors complete the LCD

From  Tom Grant 5 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  

Multiplying rational expressions made up of linear expressions

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.

From  Tom Grant 5 plays 0  

Multiplying rational expressions involving multivariate monomials

A short reminder of how to reduce first and then multiply two numerical fractions. Then we apply the same priciples to reducing like factors in an example with more than one variable and numerical…

From  Tom Grant 5 plays 0  

Simplifying a ratio of linear polynomials: 1, -1, and no simplification

This shows four examples just to cover a variety of "looks". There is at least one of each tyoe,

From  Tom Grant 11 plays 0  

Multiplication involving binomials and trinomials.

A demo of this topic where I stack the l ike terms in columns as a perform the distributions connecting each term of the first polynomial to each term in the other.

From  Tom Grant 17 plays 0  

Solving a system of linear equations using elimination with addition

This talks about why we need two equations to solve for two unknown values, and then demonstrates how to add two equations together to eliminate one varaible and solve for the other one, then find…

From  Tom Grant 12 plays 0