**Multiplying and Dividing**

Rational Expressions

Rational Expressions

**Solving Rational**

Equations

Equations

**Simplifying**

Complex

Fractions

Complex

Fractions

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**The Rational Expressions Unit Project**

by Delaney McAdams

Works Cited

Description

Example #1

Example #2

Description

Example #1

Example #2

I <3 Math

Description

Example #1

Example #2

Multiplying and dividing rational expressions is one way to help simplify expressions. Both involve multiplying expressions together straight across. Here are the steps to solve both ways:

To Multiply a rational expression:

1. Factor all numerators and denominators.

2. Cancel all common factors.

3. Either multiply the denominators and numerators together or leave the solution in factored form.

To Divide a rational expression:

1. Flip the denominator (multiply by reciprocal)

2. Follow steps 1-3 of multiplying rational expressions

14c^2d 35cd^3 24mn

------- / ------ = ------

9m^3n^2 24mn 35cd^3

336c^2dmn

16c

----------- =

----------

315m^3n^2cd^3

15d^2m^2n

2a^2 3bc^2

----- ------

5b^2c 8a^3

6a^2bc^2

3c

---------- =

------

40b^2ca^3

20ab

Solving rational equations takes one rational equation and transforms it into a linear equation. Here are the steps to solve rational equations:

Solving rational equations:

1. Simplify by removing fractions

2. Solve by substituting, adding, subtracting or whatever else applies

Simplifying complex fractions takes all of the elements of simplifying a fraction and rolls into one big fraction. Here are the steps to solving them:

To Simplify a complex fraction:

1. Find the least common denominator of all of the fractions within the problem

2. Multiply both the numerator and the denominator of the complex fraction by the LCD of the complex fraction from step 1.

3. Simplify whenever possible.

4 4 4

------- ---- ---- 4 4

16

3 3 (2) = 3-6 = -3 = -- -- =

---

-- - -- --- -- 1 -3

-3

4 2 (2) 4 4

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