To divide algebraic expressions, you can follow these steps:

1. Simplify both the numerator and denominator as much as possible by factoring out common factors or using any other applicable algebraic techniques.

2. Write the division as a fraction, with the simplified numerator as the numerator of the fraction and the simplified denominator as the denominator of the fraction.

3. To divide by a fraction, multiply by its reciprocal. In other words, if the denominator is a fraction, flip it and multiply it by the numerator.

4. Simplify the resulting expression by canceling out common factors if possible.

Here’s an example to illustrate the steps:

Divide (3x^2 + 6x) by (x + 2).

1. Simplify the numerator and denominator: 3x(x + 2) + 6(x + 2)

2. Write the division as a fraction: (3x(x + 2) + 6(x + 2)) / (x + 2)

3. Multiply by the reciprocal of the denominator: (3x(x + 2) + 6(x + 2)) * (1 / (x + 2))

4. Simplify the expression: (3x^2 + 6x + 6x + 12) / (x + 2) (3x^2 + 12x + 12) / (x + 2)

That’s the simplified division of the algebraic expressions.