Multiply and express the product in the simplest form.?

Question

1.(5/60(18/25)=3/5
2.(3m/2)(n^2/9)
3.(x/30)^3
4.(x-3/2)^3(1/x-3)^2
5.(x^2 - 9/ x+2)(x^2 - 4/ x - 3)
6.(x^2 + 5x + 4/(x + 3)^2) Divided by (x + 1/x^2 - 9)
Thnx for your help

Sorry i meant 3.(x/3)^3

Answer 1

1.(5/6)(18/25)
= (5 * 18) / (6 * 25)
= (5 * 6 * 3) / (6 * 5 * 5)
= 3 / 5

2.(3m/2)(n^2/9)
= (3 m n^2) / (9 * 2)
= (3 m n^2) / (3 * 3 * 2)
= (m n^2) / (3 * 2)
= (m n^2) / 6

3.(x/3)^3
= (x^3) / (3^3)
= x^3 / (3*3*3)
= x^3 / 27

4.(x-3/2)^3(1/x-3)^2
= [(x - 3)^3 / 2^3] * [1^2 / (x - 3)^2]
= [(x - 3)^3 * 1^2] / [2^3 * (x - 3)^2]
= (x - 3) / 2^3
= (x - 3) / 8

5.(x^2 - 9/ x+2)(x^2 - 4/ x - 3)
= [(x - 3)(x + 3) / (x + 2)] * [(x - 2)(x + 2) / (x - 3)]
= [(x - 3)(x + 3)(x - 2)(x + 2)] / [(x + 2)(x - 3)]
= (x + 3)(x - 2)
= x^2 + 3x - 2x + 6
= x^2 + x - 6

6.(x^2 + 5x + 4/(x + 3)^2) Divided by (x + 1/x^2 - 9)
= [(x + 4)(x + 1) / (x + 3)^2] / [(x + 1) / (x + 3)(x - 3)]
= [(x + 4)(x + 1) / (x + 3)^2] * [(x + 3)(x - 3) / (x + 1)]
= [(x + 4)(x + 1)(x + 3)(x - 3)] / [(x + 3)^2 (x + 1)]
= (x + 4)(x - 3) / (x + 3)

Answer 2

1.(5/60(18/25)=3/50
2.(3m/2)(n^2/9) = 3mn^2/18
3.(x/30)^3 = x^3/27,000
4.(x-3/2)^3(1/x-3)^2 = (x-3)^3/8 *1/(x-3)^2 = (x-3)/8
5.(x^2 - 9/ x+2)(x^2 - 4/ x - 3)
= (x-3)(x+3)/(x+2) *(x-2)(x+2)/(x-3) = (x+3)(x-2)
6.(x^2 + 5x + 4/(x + 3)^2) Divided by (x + 1/x^2 - 9)
=(x+1)(x+4)/(x+3)^2 * (x-3)(x+3)/(x+1)
= (x+4)(x-3)/(x+3)