Answer:
3ab + 2b + 2 - (3a)/b
Explanation:
first, multiply out brackets of both 3ab + b and 3a - b.
(3ab + b)² = 9a²b² + 3ab² + 3ab² + b²
= 9a²b² + 6ab² + b².
(3a - b)² = 9a² - 3ab - 3ab + b² = 9a² - 6ab + b².
(3ab+b)²- (3a-b)²
= (9a²b² + 6ab² + b²) - (9a² - 6ab + b²)
= 9a²b² + 6ab² - 9a² + 6ab
= 9a²b² + 6ab² + 6ab - 9a².
there's clearly factors of 3, a, b. so, factorise.
3ab (3ab + 2b + 2) - 9a².
now we can divide by 3ab:
[3ab (3ab + 2b + 2) - 9a²] / 3ab
= [3ab (3ab + 2b + 2)] / 3ab - (9a²)/3ab
= 3ab + 2b + 2 - (3a)/b