Answer:
[tex]a:b = -17:1[/tex]
Step-by-step explanation:
Given
[tex]\frac{a-3b}{a+2b} = \frac{4}{3}[/tex]
Required
Find a:b
[tex]\frac{a-3b}{a+2b} = \frac{4}{3}[/tex]
Cross Multiply
[tex]3(a-3b) = 4(a+2b)[/tex]
Open brackets
[tex]3a - 9b = 4a + 8b[/tex]
Collect Like Terms
[tex]3a - 4a = 8b+9b[/tex]
[tex]-a = 17b[/tex]
Divide through by -b
[tex]\frac{-a}{-b} = \frac{17b}{-b}[/tex]
[tex]\frac{a}{b} = \frac{17}{-1}[/tex]
[tex]\frac{a}{b} = \frac{-17}{1}[/tex]
Represent as a ratio
[tex]a:b = -17:1[/tex]
