Rational Expressions and Equations

Simplifying

100

What are the steps to simplify a rational fraction?

1) Factor

2) Cancel out fancy "ones" - same number/variable/factor on top and bottom of the fraction.

200

(10k+4) / (14K+16)

(5k + 2) / (7k + 8)

300

(63m² - 90m) / 90m²

(7m - 10) / 10m

400

(x² - 12x + 27) / (x - 9)

x - 3

500

(6x + 18) / (3x² + 16x + 21)

6 / (3x + 7)

Adding and Subtracting

100

What do you need in order to add or subtract fractions?

A Common Denominator 

200

(m+2) / (12m-16)    -     (m-1) / (12m-16)

3 / (12m-16)

300

(x + 2y) / 6y    -      5x / 3y²

(xy + 2y² - 10x) / 6y²

400

4x / (x+2)      +     3 / (x-1)

(4x² - x + 6) / (x - 1)(x + 2)

500

3/2   -   4x / (3x²+9x+6)

(9x²+19x+18) / 6(x+2)(x+1)

Multiplying and Dividing

100

How can you divide fractions?

Copy Dot Flop

200

(15b-18) / (b-9)    *     5b / (15b-18)

5b / (b-9)

300

(35x²-49x) / (x-4)    /      (5x-7)/1

7x / (x-4)

400

(15x+12) / (15x+3)     *     (5x²-14x-3) / (5x²+39x+28)

(x-3) / (x+7)

500

(5x+1) / (8n-64)     /     (35x²-23x-6) / (7x²-20x+12)

(n-2) / 8(n-8)

Solving an equation

100

Once you have a common denominator, what can you make an equation out of?

The numerators of the fractions!

200

Solve for n:

5/(4n²) + (n-2)/(4n²) = 4/n²

n = 13

300

Solve for x:

1 + (x-2)/5x  =  (x+3)/5x

x = 1

400

Solve for n:

1/(n+1) =  (2n+12)/(n²+n)  -  1/(n²+n)

n = -11

500

Solve for x:

2/(x+4) =  1/(x+3) + (5x-15)/(x²+7x+12)

x = 17/4

Excluded values

100

What are excluded values?

They make the denominator of the fractions equal to 0.

200

What are the excluded values?

5/(2x-1)(x+7)

x can't = 1/2 or -7

300

What are the excluded values?

(n+6)/(2n²+12n)

n can't = 0 and -6

400

What are the excluded values?

(n-2)/(n²+2n-8)

n can't equal 2 and -4

500

What are the excluded values?

(x²+5x-50)/(3x³+3x²-90x)

x can't equal 0, 5, or -6