(a-3b)/(a+2b) = (4)/(3) what is the value of a:b??

Question

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

what is the value of a:b??

Answer 1

Given:

`\sf (a\ -\ 3b)/(a\ +\ 2b)\ =\ (4)/(3)`

To find: The value of a:b.

Answer:

`\sf (a\ -\ 3b)/(a\ +\ 2b)\ =\ (4)/(3)`

Cross-multilpying,

`\sf 3\ *\ (a\ -\ 3b)\ =\ 4\ *\ (a\ +\ 2b)\\\\3a\ -\ 9b\ =\ 4a\ +\ 8b`

Bringing the like terms together,

`\sf 3a\ -\ 4a\ =\ 8b\ +\ 9b\\\\\\-a\ =\ 17b\\\\\\(-a)/(b)\ =\ 17\\\\\\(a)/(b)\ =\ -17`

Therefore, a:b = -17.