Multiply 2 (x+3) / x (x-1) * 4x (x+2) / 10 (x+3)

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

Step-by-step explanation:

Simplify the following:

(2*4 x (x + 3) (x - 1) (x + 2) (x + 3)) / (10 x)

((x - 1) * 4*2 (x + 3) x (x + 2) (x + 3)) / (x*10) = x/x * ((x - 1) * 4*2 (x + 3) (x + 2) (x + 3)) / 10 = ((x - 1) * 4*2 (x + 3) (x + 2) (x + 3)) / 10:

(4*2 (x - 1) (x + 3) (x + 2) (x + 3)) / 10

The gcd of 4 and 10 is 2, so ((x - 1) * 4*2 (x + 3) (x + 2) (x + 3)) / 10 = ((2*2) 2 (x - 1) (x + 3) (x + 2) (x + 3)) / (2*5) = 2/2 * (2*2 (x - 1) (x + 3) (x + 2) (x + 3)) / 5 = (2*2 (x - 1) (x + 3) (x + 2) (x + 3)) / 5:

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

Combine powers. (2*2 (x - 1) (x + 3) (x + 2) (x + 3)) / 5 = (2*2 (x - 1) (x + 3) ^ (1 + 1) (x + 2)) / 5:

(2*2 (x + 3) ^ (1 + 1) (x - 1) (x + 2)) / 5

1 + 1 = 2:

(2*2 (x - 1) (x + 3) ^2 (x + 2)) / 5

2*2 = 4:

Answer: (4 (x - 1) (x + 3) ^2 (x + 2)) / 5