Questions about Algebra.

Question

Please bear for my long questions here, but I literally need our help in my assignment.

Graph the linear system and determine how many solutions it has: no solution, exactly one solution or
infinitely many solutions. (How do you graph this? Can you provide a graph for this?)

a. x + y = 4
x - y = 2

b. x + 2y = -2
-3x - 6y = 6

c. 2x - 3y = -6
-3y + 2x = 3

Multiplying rational expressions: (I will just write divided by as the operation used)

1. w^3-1/(w-1)^2   *   w^2-1/w^2+w+1
2. 19x^2/12y-1   *   1-12y/3x
3. 10x-4x^2/4x^20x+25   *   (2x^3-5x^2)
4. a^2-2ab+b^2/a-b T  *   (a+b)^3/a^2+2ab+b^2

Dividing rational expresseion:

1. x^2+6x+9/18 DIVIDED BY (x+3)^2/36
2. 2x^2-5x-12/6+4x DIVIDED BY x^2-16/2

THIS ONE IS A COMPLEX FRACTION
1. x^2+5x+6/x+2/x+3

2. 10/a+b/5

Answer 1

1)( x^2+6x+9)/18  /  (x+3)^2/36

     x^2+6x+9=(x+3)^2

    (x+3)^2/18  *  36/(x+3)^2=36/18=2

 

2) I'll factor the terms for you.

 

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

 Do you see the common factors ?