Rational Review

Multiply/Divide

100

1/3 * 5/9

5/27

200

What you do when you divide fractions. 

What is “keep change flip”?

300

Multiply and simplify:

(6x^2-18x)/(x^2-10x+21)*(x^2-14x+49)/(3x^2)

(2(x-7))/x

400

{(3x+27)}/{(6x-48)}-:(x^2+9x)/(x^2-4x-32)

(x+4)/(2x)

500

(x+7)/(x+8) *(x^2+x-56)/(x^2-49)

1

Add/Subtract

100

(9)/(10)-(1)/(5)

7/10

200

What you must have if you want to add or subtract fractions.

What is a Common Denominator?

300

Add the rational expressions:

(x+1)/(x^2-9) + (x+7)/(x^2-9)

(2x+8)/(x^2-9)

400

Subtract the rational expressions:

(4)/(x+4)-(3)/(4)

(4-3x)/{4(x+4)}

500

(4)/(3x+3)+(1)/(x-2)

(7x-5)/(3(x+1)(x-2)

Solve it!

100

Excluded values of a rational expression will make the value of the denominator equal to this number.

What is 0?

200

Solve the equation:

(5)/(x)=(7)/(x+2)

x=5

300

(x+4)/(4)+(x-1)/(4)=(x+4)/(4x)

x=-2

x=1

400

Solve  1=1/(x^2+2x)+(x-1)/x

x= -1

500

Solve and check for extraneous solutions:

(x+11)/(x^2-5x+4)=5/(x-4)-3/(x-1)

x=4

is extraneous so No Solution

Random but Relevant

100

Factor:

4x^2+4x

4x(x+1)

200

What is the domain restriction given:

(5)/(x)=(7)/(x+2)

x!= 0 or -2

300

Simplify the rational expression and state any restrictions:

(x^2+5x-14)/(x^2-4x+4)

(x+7)/(x-2)

x!=2

400

Factor

 2x^2-2

2(x+1)(x-1)

500

Find the common denominator of the rational expression:

(2p)/(p+6)  and  2/(5p-4)

(p+6)(5p-4)