Simplify f(x) = the quantity 3 x-squared minus 4x plus 1 all over 3x minus 1. Using complete sentences, explain why f(1) = 0, f(0) = -1, and f(-1) = -2, yet f(o

Question

1. Simplify f(x) = the quantity 3 x-squared minus 4x plus 1 all over 3x minus 1. Using complete sentences, explain why f(1) = 0, f(0) = -1, and f(-1) = -2, yet f(one-third) is undefined. Make sure to show your work.

 

2. Show all work in dividing the quantity y-squared minus 3y plus 2 all over the quantity y-squared plus 5y plus 6 by the quantity y-squared plus 2y minus 8 all over the quantity y-squared plus y minus 12 . Use complete sentences to explain how to simplify this expression.

 

3. Show all work to simplify 2 over x + 2 over x plus 1 - 2 over x plus 2. Use complete sentences to explain how to simplify this expression. Remember to list all restrictions.

 

4. Are the complex fractions the quantity x-squared minus x minus 20 over 4 all over the quantity x minus 5 over 10 and the quantity x-squared minus x minus 20 over x minus 5 all over the quantity 4 over 10 equivalent? Simplify each, and then explain why or why not.

 

5.Show all work to simplify 1 over x plus 3 over 8=1 over 2. Use complete sentences to explain how to simplify this expression.

Answer 1

3x^2-4x+1/3x-1

Factorize quadratric expressions

(3x-1)(x-1)/3x-1...

 

this is will cancel out 3x-1 as they are same 

 

leaving x-1

 

so when f=1

1-1=0

 

when f=0

0-1=-1

 

when f=-1

-1-1=-2