How to divide rational expressions

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Simplifying Rational Expressions Involving Division
State the restrictions on the variables, then simplify.

$\large \frac{81x}{64y^2} \div \frac{27x^2}{32y}$ $\frac{81 x}{64 y ^{2}} \div \frac{27 x ^{2}}{32 y}$
Simplifying Rational Expressions Involving both Multiplication and Division
State the restrictions on the variables, then simplify.
1. $\frac{72x^4y^2}{8x^5z^3} \times \frac{y^2}{x^3} \div \frac{15x^4y^4}{15z^4}$
2. $\frac{15x^4y^4}{18x^2z^7} \times \frac{5z^3}{5x^3y} \div \frac{25x^2y}{50z^5}$
Dividing Rational Expressions in Factored Form
State the non-permissible values for x, then simplify:

$\large \frac{(x+2)}{(x-5)(x+4)} \div \frac{3(x+2)}{(x+4)(x)}$ $\frac{( x + 2 )}{( x - 5 ) ( x + 4 )} \div \frac{3 ( x + 2 )}{( x + 4 ) ( x )}$
Convert Expressions to Factored Form, then Divide
State the non-permissible values for x, then simplify:

$\large \frac{3x^2-12x}{x^2-4} \div \frac{2x^3-8x^2}{x^2-x-6}$ $\frac{3 x ^{2} - 12 x}{x ^{2} - 4} \div \frac{2 x ^{3} - 8 x ^{2}}{x ^{2} - x - 6}$
Fractions Dividing Fractions
State the non-permissible values for x, then simplify:

$\large \frac{ \frac{25x+10}{4x-10}}{\frac{25x^2+10x}{(2x-5)^2}}$ $\frac{\frac{25 x + 10}{4 x - 10}}{\frac{25 x ^{2} + 10 x}{( 2 x - 5 ) ^{2}}}$
Performing Addition First, then Division
Simplify:

$\large \frac{\frac{3}{2a+6}+\frac{4}{4a-4}}{\frac{3}{a}+5}$ $\frac{\frac{3}{2 a + 6} + \frac{4}{4 a - 4}}{\frac{3}{a} + 5}$

Dividing rational expressions