Help with division? (steps please)

Question

The equation is (x^6y^6-x^3y^3)/x^3y^3

The answer is x^3-1+(y^9)/x^3

How do I get to the answer?

 

The equation is (-16y^3+24y^4)/(-4y^2)

The answer is 4y-6y^2

 

The equation is (-20a^2b+12ab^2)/(-4ab)

The answer is 5a-3b

 

The equation is (3x^2y+6x^2y^2+3xy)/(3xy)

The answer is 2xy+x+1

Answer 1

The equation is (x^6y^6 - x^3y^3)/x^3y^3

Distribute x^3y^3

(x^6y^6)/ x^3y^3 - (x^3y^3)/x^3y^3

Cacel common terms

(x^6y^6)/ x^3y^3 - 1

Recall a^m/a^n = a ^(m-n)

x^6/x^3 = x^(6-3) = x^3

y^6/y^3 = y^(6-3) = y^3

Answer is x^3^y3 - 1

Answer 2

The equation is (-16y³+24y⁴)/(-4y²)

 Distribute -4y²

 = (-16y³)/ (-4y²) + (24y⁴)/(-4y²)

 Cacel common terms

  = 4y³/ y² + (-6y⁴)/y²

Recall a^m/aⁿ = a ^(m-n)

y³/y² = y^(3-2)   = y

y⁴/y² = y^(4-2)   = y²

Answer is   = 4y -6y²

Answer 3

The equation is (-20a²b+12ab²)/(-4ab)

Distribute -4ab

 = (-20a²b) / (-4ab) + (12ab²)/(-4ab)

Cacel common terms

= (5a²b) / ab) - (3ab²/ab)

Cancel common terms ab in numerator and denominator

Answer is     = 5a - 3b 

Answer 4

The equation is (3x²y + 6x²y² + 3xy ) / (3xy)

Distribute 3xy

=(3x²y/ 3xy) + (6x²y² / 3xy) + (3xy/ 3xy)

Cancel common terms 3xy 

= x + 2xy + 1