R7 Rational Expressions. Rational Expressions An expression that can be written in the form P/Q,...
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Transcript of R7 Rational Expressions. Rational Expressions An expression that can be written in the form P/Q,...
![Page 1: R7 Rational Expressions. Rational Expressions An expression that can be written in the form P/Q, where P and Q are polynomials and Q is not equal to zero.](https://reader030.fdocuments.us/reader030/viewer/2022032607/56649edb5503460f94beb78d/html5/thumbnails/1.jpg)
R7 Rational
Expressions
![Page 2: R7 Rational Expressions. Rational Expressions An expression that can be written in the form P/Q, where P and Q are polynomials and Q is not equal to zero.](https://reader030.fdocuments.us/reader030/viewer/2022032607/56649edb5503460f94beb78d/html5/thumbnails/2.jpg)
Rational Expressions
An expression that can be written in the form P/Q, where P and Q are polynomials and Q
is not equal to zero.
![Page 3: R7 Rational Expressions. Rational Expressions An expression that can be written in the form P/Q, where P and Q are polynomials and Q is not equal to zero.](https://reader030.fdocuments.us/reader030/viewer/2022032607/56649edb5503460f94beb78d/html5/thumbnails/3.jpg)
Rational Expressions1. Factor each expression completely
2. List any restrictions on the variables in the denominator
3. Divide out any common factors
4. Simplify and leave your answer in factored form
![Page 4: R7 Rational Expressions. Rational Expressions An expression that can be written in the form P/Q, where P and Q are polynomials and Q is not equal to zero.](https://reader030.fdocuments.us/reader030/viewer/2022032607/56649edb5503460f94beb78d/html5/thumbnails/4.jpg)
Simplify each rational expression and list any
restrictions
![Page 5: R7 Rational Expressions. Rational Expressions An expression that can be written in the form P/Q, where P and Q are polynomials and Q is not equal to zero.](https://reader030.fdocuments.us/reader030/viewer/2022032607/56649edb5503460f94beb78d/html5/thumbnails/5.jpg)
Simplify each rational expression and list any
restrictions
![Page 6: R7 Rational Expressions. Rational Expressions An expression that can be written in the form P/Q, where P and Q are polynomials and Q is not equal to zero.](https://reader030.fdocuments.us/reader030/viewer/2022032607/56649edb5503460f94beb78d/html5/thumbnails/6.jpg)
Multiplying and Dividing Rational
Expressions1. Change division to multiplication
of inverse
2. Factor each expression completely
3. Divide out any common factors
4. Simplify and leave answer in factored form
![Page 7: R7 Rational Expressions. Rational Expressions An expression that can be written in the form P/Q, where P and Q are polynomials and Q is not equal to zero.](https://reader030.fdocuments.us/reader030/viewer/2022032607/56649edb5503460f94beb78d/html5/thumbnails/7.jpg)
Perform the indicated operation and simplify
![Page 8: R7 Rational Expressions. Rational Expressions An expression that can be written in the form P/Q, where P and Q are polynomials and Q is not equal to zero.](https://reader030.fdocuments.us/reader030/viewer/2022032607/56649edb5503460f94beb78d/html5/thumbnails/8.jpg)
Perform the indicated operation and simplify
![Page 9: R7 Rational Expressions. Rational Expressions An expression that can be written in the form P/Q, where P and Q are polynomials and Q is not equal to zero.](https://reader030.fdocuments.us/reader030/viewer/2022032607/56649edb5503460f94beb78d/html5/thumbnails/9.jpg)
Perform the indicated operation and simplify
![Page 10: R7 Rational Expressions. Rational Expressions An expression that can be written in the form P/Q, where P and Q are polynomials and Q is not equal to zero.](https://reader030.fdocuments.us/reader030/viewer/2022032607/56649edb5503460f94beb78d/html5/thumbnails/10.jpg)
Perform the indicated operation and simplify
![Page 11: R7 Rational Expressions. Rational Expressions An expression that can be written in the form P/Q, where P and Q are polynomials and Q is not equal to zero.](https://reader030.fdocuments.us/reader030/viewer/2022032607/56649edb5503460f94beb78d/html5/thumbnails/11.jpg)
Adding and Subtracting
Rational Expressions1. Factor each denominator completely
2. Find the LCM of the denominators
3. Multiply each term by the LCM
4. Simplify the numerator
5. The denominator is the LCM
6. Simplify and leave your answer in factored form
![Page 12: R7 Rational Expressions. Rational Expressions An expression that can be written in the form P/Q, where P and Q are polynomials and Q is not equal to zero.](https://reader030.fdocuments.us/reader030/viewer/2022032607/56649edb5503460f94beb78d/html5/thumbnails/12.jpg)
Perform the indicated operation and simplify
![Page 13: R7 Rational Expressions. Rational Expressions An expression that can be written in the form P/Q, where P and Q are polynomials and Q is not equal to zero.](https://reader030.fdocuments.us/reader030/viewer/2022032607/56649edb5503460f94beb78d/html5/thumbnails/13.jpg)
Perform the indicated operation and simplify
![Page 14: R7 Rational Expressions. Rational Expressions An expression that can be written in the form P/Q, where P and Q are polynomials and Q is not equal to zero.](https://reader030.fdocuments.us/reader030/viewer/2022032607/56649edb5503460f94beb78d/html5/thumbnails/14.jpg)
Perform the indicated operation and simplify
![Page 15: R7 Rational Expressions. Rational Expressions An expression that can be written in the form P/Q, where P and Q are polynomials and Q is not equal to zero.](https://reader030.fdocuments.us/reader030/viewer/2022032607/56649edb5503460f94beb78d/html5/thumbnails/15.jpg)
Perform the indicated operation and simplify
![Page 16: R7 Rational Expressions. Rational Expressions An expression that can be written in the form P/Q, where P and Q are polynomials and Q is not equal to zero.](https://reader030.fdocuments.us/reader030/viewer/2022032607/56649edb5503460f94beb78d/html5/thumbnails/16.jpg)
Perform the indicated operation and simplify
![Page 17: R7 Rational Expressions. Rational Expressions An expression that can be written in the form P/Q, where P and Q are polynomials and Q is not equal to zero.](https://reader030.fdocuments.us/reader030/viewer/2022032607/56649edb5503460f94beb78d/html5/thumbnails/17.jpg)
Complex Rational Expressions
1. Factor each denominator completely
2. Find the LCM
3. Multiply numerator/denominator by LCM
4. Combine your like terms
5. Simplify and leave your answer in factored form
![Page 18: R7 Rational Expressions. Rational Expressions An expression that can be written in the form P/Q, where P and Q are polynomials and Q is not equal to zero.](https://reader030.fdocuments.us/reader030/viewer/2022032607/56649edb5503460f94beb78d/html5/thumbnails/18.jpg)
Perform the indicated operation and simplify
![Page 19: R7 Rational Expressions. Rational Expressions An expression that can be written in the form P/Q, where P and Q are polynomials and Q is not equal to zero.](https://reader030.fdocuments.us/reader030/viewer/2022032607/56649edb5503460f94beb78d/html5/thumbnails/19.jpg)
Perform the indicated operation and simplify
![Page 20: R7 Rational Expressions. Rational Expressions An expression that can be written in the form P/Q, where P and Q are polynomials and Q is not equal to zero.](https://reader030.fdocuments.us/reader030/viewer/2022032607/56649edb5503460f94beb78d/html5/thumbnails/20.jpg)
Perform the indicated operation and simplify