Question

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

Answer 1

Answer:

(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