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Master Simplifying Rational Expressions: Step-by-Step Guide

Derive proofs that involve the properties of angles and triangles

Classifying triangles

Isosceles and equilateral triangles

Pairs of lines and angles

Parallel lines and transversals

Parallel line proofs

Perpendicular line proofs

Solve problems that involve the properties of angles and triangles

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Angles in a circle

Angle in standard position

Coterminal angles

Coterminal Angles

Reference angle

Circles and circumference

Circle properties

Arcs of a circle

Areas and sectors of circles

Solve problems that involve the cosine law and the sine law including the ambiguous case

Introduction to bearings

Bearings and direction word problems

Bearings and Direction Word Problems

Angle of elevation and depression

Law of sines

Ambiguous case: SSA triangles

Law of cosines

Applications of the sine law and cosine law

Find the exact value of trigonometric ratios

ASTC rule in trigonometry (All Students Take Calculus)

ASTC rule in trigonometry

Analyze and prove conjectures using logical reasoning to solve problems

Set notation

Understanding How to Use Set Notation

Set builder notation

Intersection and union of 2 sets

Intersection and Union of 2 Sets

Intersection and union of 3 sets

Intersection and Union of 3 Sets

Solving radical equations

Solving Radical Equations Involving One Square Root Term

Solving Radical Equations Involving More than One Square Root Term

Factor by taking out the greatest common factor

Factor by taking out GCF

Factor by grouping

Analyze puzzles and games that involve numerical reasoning using problem-solving strategies

Factoring difference of cubes

Factoring sum of cubes

Factoring difference of squares: \(x^2 - y^2\)

Factoring difference of squares: <katex>x^2 - y^2</katex>

Factoring difference of squares: x^2 - y^2

Factoring trinomials

Factoring Trinomials

Arithmetic sequences

Arithmetic series

Arithmetic series formula

Geometric sequences

Geometric series

Geometric Series

Addition rule for 

Addition Rule for "OR"

Addition rule for "OR"

Multiplication rule for 

Multiplication rule for "AND"

Multiplication Rule for "AND"

Conditional probability

Probability involving permutations and combinations

Analyze costs and benefits of renting, leasing and buying

Taxes, discounts, tips and more

Discounts — Word Problem

Taxes — Word Problem

Percentage - Applying a Discount Price– Word Problem

Percentage - Applying a Discount Percent – Word Problem

Percentage - Applying a Tax Total – Word Problem

Percentage - Applying a tax Percent – Word Problem

Simple interest

Simple Interest — Word Problem

Basic Concepts of Simple Interest – Word Problem

Borrowing Money for More Than One Year  – Word Problem

Investigate the Advantages of Borrowing Money  – Word Problem

Linear independence

Simplifying rational expressions and restrictions

Adding and subtracting rational expressions

Adding and Subtracting Rational Expressions

Multiplying rational expressions

Multiplying Rational Expressions

Multiplying Rational Expressions in Factored Form

Dividing rational expressions

Dividing Rational Expressions

Dividing Rational Expressions in Factored Form

Applications of rational equations

Finance: Compound interest

Finance: Compound Interest

Continuous growth and decay

Finance: Future value and present value

Analyze an investment portfolio in terms of interest rate rate of return total return

Image and range of linear transformations

Infinite geometric series

Logarithmic scale: Richter scale (earthquake)

Logarithmic scale: pH scale

Logarithmic scale: dB scale

Sigma notation

Solve problems that involve personal budgets

Properties of linear transformation

Applications of linear equations

Graphing reciprocals of linear functions

Exponential growth and decay by a factor

Exponential decay: Half-life

Exponential growth and decay by percentage

Graphing reciprocals of quadratic functions

Model and solve problems that involve systems of linear inequalities in two variables

What is linear programming?

Finding Optimal Values Given Constraints In Slope-Intercept Form

Finding Optimal Values Given Constraints In Standard Form

Linear programming word problems

System of linear equations

System of linear-quadratic equations

Graphing linear inequalities in two variables

Graphing quadratic inequalities in two variables

Graphing systems of quadratic inequalities

Graphing systems of linear inequalities

Applications of inequalities

Demonstrate understanding of characteristics of quadratic functions

Introduction to quadratic functions

Characteristics of quadratic functions

Transformations of quadratic functions

Quadratic function in general form: y = ax^2 + bx + c

Converting from general to vertex form by completing the square

Shortcut: Vertex formula

Converting general form into vertex form by applying the vertex formula

Vertex Formula Application

Graphing quadratic functions: General form VS. Vertex form

Finding the quadratic functions for given parabolas

Applications of quadratic functions

Quadratic function in vertex form: y = a(x-p)^2 + q

Completing the square

Completing the Square

Foundations of Mathematics 110

Logical Reasoning

Number

Relations and Functions

math

Intro

A rational expression is a fraction that its numerator and/or <a href='[[glossary.html|{"keyword":"Denominator","term":"Denominator"}]]'>denominator</a> are polynomials. In this lesson, we will first learn how to find the non-permissible values of the variable in a rational expression. Then, we will how to simplify rational expressions.

Simplifying algebraic fractions and restrictions

Rules to simplifying rational expressions

Common factors of polynomials

Factoring polynomials: \(ax^2 + bx + c\)

Factoring perfect square trinomials: (a + b)^2 = a^2 + 2ab + b^2 or (a - b)^2 = a^2 - 2ab + b^2

Find the difference of squares: (a - b)(a + b) = (a^2 - b^2)

Solving polynomial equations