(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

`a:b = -17:1`

Explanation:

Given

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

Required

Find a:b

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

Cross Multiply

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

Open brackets

`3a - 9b = 4a + 8b`

Collect Like Terms

`3a - 4a = 8b+9b`

`-a = 17b`

Divide through by -b

`(-a)/(-b) = (17b)/(-b)`

`(a)/(b) = (17)/(-1)`

`(a)/(b) = (-17)/(1)`

Represent as a ratio

`a:b = -17:1`