Choose a Topic Difference of Cubes Sum of Cubes Rational Expressions and NPV’s Adding and Subtracting Rational Expressions Multiplying and Dividing Rational Expressions

Difference of Cubes

Practice

Difference of Cubes

Practice

Difference of Cubes Difference of Cubes Versus Sum of cubes

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Difference of cubes Versus Sum of cubes  Since these two are so similar it is easy to mix them up, so here’s a trick to remember the difference  Look at the sign in the original binomial  The first sign in the factors is the same  The second sign is the opposite sign  The third sign is always (+) a^3 ± b^3 = (a [same sign] b)(a^2 [opposite sign] ab [always positive] b^2)

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Sum of Cubes

Practice

Sum of cubes Step 1: identify the cube roots of both terms x and y2 and 3y 2: substitute in one cube root for all the x’s and the other root for all the y’s 3: simplify (if possible) Not possible to simplify

Practice

Why it works Difference of Cubes Versus Sum of Cubes

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Rational expressions

Non-permissible Values

How to find NPV’s

Finding NPV’s

Example

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Adding and Subtracting Rational Expressions  The first rule of adding and subtracting rational expressions is to treat them just like regular fractions: First you use equivalent fractions to make both fractions have the same denominator and then you add or subtract the numerators without changing the denominators

How to guide Step 1: achieve common denominators (Factoring the denominators can help you do this if you are stuck) 2: add the numerators; the denominators stay the same *The same method works for subtraction

Something to note…  Most questions will ask you to find the NPV’s. Remember to always look for NPV’s at EVERY step of the question: Before you do anything, after the denominators are the same, after you have added and subtracted the numerators, and even after you factor the final answer Learn about NPV’s

Practice

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Multiplying and Dividing Rational Expressions  The first rule for multiplying and dividing rational expressions is to treat them like fractions

Multiplication

Division

Something to note…  In many questions involving the multiplication or division of rational expressions, you will be asked to find NPV’s. Make sure that you look for NPV’s in ALL steps, before you multiply and divide and after. Even factor everything at the end to make sure that you found all of the NPV’s. Learn about NPV’s

Practice

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