Solving rational expressions
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The document provides instructions and examples for solving rational equations and inequalities. It explains that rational equations can be solved by multiplying both sides by the least common denominator to eliminate fractions. Students are advised to check their solutions and watch out for extraneous solutions. The steps for solving rational inequalities are given as identifying domain restrictions, moving everything to one side, solving, and drawing vertical lines to indicate intervals on the number line. Some sample problems are worked through as examples.
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Rational equations are equations where a variable occurs in the denominator of a rational expression. To solve rational equations:
1) Identify values that result in no solution by finding values where the denominator equals 0.
2) Find the lowest common denominator (LCD) and multiply both sides of the equation by the LCD.
3) Solve the numerators and reject any solutions that result in the denominator equaling 0.
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Hprec2 1
This document discusses two graphical methods for approximating solutions to equations: the intersect method and the x-intercept method.
The intersect method involves graphing both sides of the equation on the same coordinate plane and finding the x-coordinates where the graphs intersect. The x-intercept method rewrites the equation in the form f(x)=0, graphs the function, and uses the calculator to find the x-intercepts or zeros of the function.
Examples are provided to demonstrate both methods. Key steps are outlined, such as setting the calculator to the correct mode and using appropriate functions to find intersections or zeros.
Algebraic fractions
This document provides information and examples about algebraic fractions, including:
- Simplifying and reducing rational expressions by dividing both the numerator and denominator by common factors.
- Multiplying, dividing, adding, and subtracting rational algebraic expressions by using common denominators.
- Finding the least common multiple of denominators.
- Solving rational equations by clearing fractions, combining like terms, and isolating the variable.
variables_expressions
This document defines key terms related to variables and expressions:
- A variable represents an unknown number using a symbol like x or n.
- A variable expression contains variables and numbers with arithmetic operations but no equal sign, like n - 5.
- To evaluate an expression means to substitute numbers for the variables and simplify the result.
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MIT Math Syllabus 10-3 Lesson 3: Rational expressions
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Skills practice constant rate of change
Skills Practice
Constant Rate of Change
Find the constant rate of change for each table
Find the constant rate of change for each graph
Rate of change
Essential Question How can you find the unit rate from a line on a graph that goes through the origin?
Objective understand slope as it relates to rate of change
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The document provides instruction and practice problems for students on several math topics:
1) Finding the difference and product of integers.
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7th daily 10 10-14 proportions vocabulary and long division
This document contains bell work, notes, and assignments on several math topics:
1) Solving problems involving integers, long division, and proportions.
2) Students are asked to complete graphic organizers on vocabulary words, practice long division, and solve practice proportion problems using cross products.
3) An exit ticket asks students to summarize the main concepts covered which included applying long division, proportions, and seeing how these topics apply to the real world.
Part 1: Vocabulary; How do you solve proportions?
I will
Add/Subtract/Multiply/Divide Integers
Apply and explore math vocabulary involved in proportions.
How do you solve proportions?
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Real numbers
This document discusses classifying real numbers as rational or irrational. It provides examples of classifying numbers such as 5, -12.75, and fractions like 16/4. Additional examples classify numbers such as 21, 0/3, and 4/0 as rational, irrational, or not real numbers. The document also discusses comparing and ordering rational and irrational numbers by converting them to the same form. It provides examples of ordering numbers like 1/4, 75%, 0.04, 10%, and 9/7 from least to greatest. In the study section, it lists topics to review such as estimating square roots, perfect squares and cubes, comparing numbers, number sets, and real numbers.
Cubes
This document discusses cubes and cube roots. It defines a perfect cube as a number that is the cube of an integer. Perfect cubes have integer cube roots. The document provides examples of determining if a number is a perfect cube and finding the cube root of perfect cubes. It also discusses the relationships between side lengths, volumes, and cube root operations for cubes.
Square and square roots
This document provides an overview of squaring numbers and finding square roots. It discusses key concepts such as:
- Squaring a number means multiplying a number by itself
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- Examples are provided of finding the square of numbers and the square roots of perfect squares.
Jeopardy laws of exponents
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Compute with scientific notation
1) Scientific notation is a way of writing numbers in the form c × 10n, where c is between 1 and 10 and n is an integer.
2) Scientific notation allows very large and very small numbers to be written easily without lots of zeros by moving the decimal point and changing the exponent.
3) Operations like multiplication and division with scientific notation follow the normal rules of exponents - the exponents are added or subtracted.
Scientific notation ppt
Scientific notation is used to write very large or very small numbers in a standardized way. It involves writing a number between 1 and 10 multiplied by a power of 10. This allows mathematicians to easily work with numbers that would otherwise be long to write out. Some examples of converting between scientific notation and standard form are given.
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Solving rational expressions
- 1. 9.6 Solving Rational Equations p.505
- 3. Example : Solve. LCD : 2x Multiply each fraction through by the LCD Check your solution!
- 4. Solve. LCD : ? LCD : (x+1) Check your solution! ? No Solution!
- 5. Solve. Factor 1 st ! LCD: (x+2)(x-2) Check your solutions!
- 7. Example : Solve. Check your solutions!
- 8. Last Example : Solve. Check your solutions!
- 9. Solve for x (alternate method): Multiply through by a common denominator to get rid of all fractions
- 14. One more SAT Question If Which of the following is an expression for
- 15. Now you try! Pg 509 #’s 6-9 all