Rationals

Vocabulary

100

the dividend of a division; goes to the upper part of a fration

What is a numerator?

200

the divisor of a division; goes to the lower part of a fration

What is a denominator?

300

an expression that has multiple terms and variables that cannot be simplied any more

What is "polynomial"?

400

An algebraic fraction with a numerator and a denominator that are polynomial

What is "rational expression"?

500

What is a restricted value? What are the restricted values of x/(x^2-4)(x+3)?

any value for a variable that makes an expression undefined； x ≠ ±2，x ≠ -3

+ & — rational expression

100

Write answer in simplest form. Determine all non-permissible values. 2/x+3/x

5/x x≠0

200

Write answer in simplest form. Determine all non-permissible values. 3/x-10/y

3y-10x/xy x≠0, y≠0

300

Write answer in simplest form. Determine all non-permissible values. 31/(5x+10) + x/(x+2)

31-5x/5(x+2) x≠-2

400

Write answer in simplest form. Determine all non-permissible values. x-3/(x^2-5x-6) - x-6/(x^2-2x-3)

3(2x-9)/(x+1)(x-6)(x-3) x≠-1,6,3

500

Write answer in simplest form. Determine all non-permissible values. 3t+15/(2t^2+13t+15) - 2t-3/(t^2-16)

-t^2-39/(2t+3)(t^2-16) t≠-5, -4, -1.5, 4

x & / rational expression

100

Write your answer in simplest form. Identify all non-permissible values. (3x/4y)*(2x/3y)/(4x/12y)

2/3 (x=/0,y=/0)

200

Write your answer in simplest form. Identify all non-permissible values. (x^2 - x - 6)/(x^2 - 9)*(x^2 - 2x - 3)/(x^2+x -2)

(x+2)/x (x/=3,-2,-3,-1,1)

300

Write your answer in simplest form. Identify all non-permissible values. (a^2-9)/(a^2-a-6)/(a^2+7a+12)/(a^2-4)

1/(a+4) (x/=3,-3,2,-2,-4)

400

(x^2+2x+1)/(x^2-2x+1)*(x^2-x-6)/(x^2-1)/(x^2-2x-3)/(x^2-2x+1)

(x+2)/(x-1) (x/=1,-1,3,-2)

500

Write your answer in simplest form. Identify all non-permissible values. (4x^-6x-20)/(4x^2+10x-24)*(4x^-30x+36)/(4x^2-14x-60)/(x-8)/(x+4)

0 (x/=-2.5,8,-1.5,6,1.5,-4)