Pleas help with this Question.?

Question

Can you explain it step by step.

7x+21 over 35x times 5x-15 over x^2 -9

Answer 1

7x+21/35x * 5x-15/x^2-9
a) simplify the 7x/35x.
b) 7x is the common factor between 7x and 35x.
c) 7x/35x = 1/5, because the x/x becomes 1, and 7/35 * 1 = 7/35, so ...
d) 1/5 +21 * 5x-15/x^2-9
e) do the same thing: that x^2 becomes x, because x * x = x.
f) x/x = 1, so 5(1) = 5.
g) 1/5 + 21 * 5-15-9
h) on the right side of the symbol, simplify the 5-15-9.
i) 5-15 = -10. -10-9 = -19.
j) 1/5 + 21 * -19.

Answer 2

(i) (7x + 21)/35 = (7x + 7*3)/(7 * 5) = (x + 3)/5

(ii) (5x - 15)/(x^2 - 9) = (5x - 5*3) / [(x - 3)(x + 3)] =

= 5(x - 3)/[(x - 3)(x + 3)] = 5/(x + 3)
[Note: x cannot be 3]

From (i) + (ii) we get
(7x + 21)/(35x) * (5x - 15)/(x^2 - 9) =
= (x + 3)/(5x) * 5/(x + 3) = 1/x

From 5/(x + 3) we get that x cannot be -3
x is not in {0,-3,3} and the answer is 1/x

Answer 3

(7x+21)/ 35x * (5x-15)/( x^2 -9)
= 7(x+3)/7*5x * 5(x-3)/(x-3)(x+3)
= (x+3)/5x * 5/(x+3)
= 5(x+3)/5x(x+3)
= 1/x

Answer 4

7x+21 = 7(x+3) and 5x-15=5(x-3) and x²-9=(x+3)(x-3)
so
7(x+3)/35x * 5(x-3)/(x+3)(x-3)
7(x+3)*5(x-3)/35x(x+3)(x-3) = x