for all integers a, b, c, If a/b - 2c and a/2b + 3c then a/b and a/c

Thanks for your help.

To find the values of a/b and a/c, we can solve the given equations simultaneously.

Given:
1) a/b - 2c
2) a/2b + 3c

To solve these equations, we need to eliminate one variable (either a or b) from both equations. Let's eliminate the variable 'a'.

Multiplying equation 1 by 2 and equation 2 by b, we get:

1) 2(a/b) - 4c
2) (a/b) + 3bc

Now, let's equate both the equations:

2(a/b) - 4c = (a/b) + 3c

Now, we can solve this equation to find the value of a/b.

2(a/b) - (a/b) = 4c + 3c

Simplifying,

(a/b) = 7c

Therefore, a/b = 7c.

To find the value of a/c, substitute the value of a/b back into one of the original equations. Let's use equation 1:

a/b - 2c = 7c - 2c = 5c

Therefore, a/c = 5c.

In conclusion, we have found the values of a/b and a/c:
a/b = 7c
a/c = 5c