Math help factor problems?

Question

Factor math questions that i really need help on..

1. X^2 +x / x^2 times 3x – 3/ x^2 – 1
A. x+1/ x
B. 3
C. 0
D. 3/x

2. 6x^2 / 5x^2 times x+3/3
A. 2(x+3) / 5
B. x+3/ 3
C. 2(x + 3)
D. x+3 / 15

3. 4a+4 / 4 divide a+1/6
A. a(a+1)^2 /6
B. a(a+1)6
C. 6
D. 24

4. 5x – 15 / 10
A. 3x
B. x- 3 / 2
C. x-15 / 2
D. 2x -3

Answer 1

1.) (X^2 +x) / (x^2) times (3x – 3)/ (x^2 – 1)
Factor:
x^2 + x = x(x + 1)
3x - 3 = 3(x - 1)
x^2 - 1 = (x + 1)(x - 1)

Put it together:
x(x + 1) / x^2 * 3(x - 1)/(x + 1)(x - 1)

Cancel:
(x + 1) / x * 3/(x + 1)

Multiply:
3(x + 1) / x(x + 1) = 3/x (d)

2.) 6x^2 / 5x^2 * (x+3)/3
This one's simple: the x^2 in the first fraction cancels.
6/5 * (x+3)/3
2(x + 3)/5 (a)

3.) (4a+4) / 4 divide (a+1)/6
Flip the second fraction and cancel the 4 in the first fraction:
(a + 1) * 6/(a+1)
Simplify:
6 (C)

4.) (5x – 15) / 10
5(x - 3)/10
(x - 3)/2 (b)