11.2 Homework Problems: Multiplying and Dividing Rational Expressions
1. Multiply the following rational expressions and simplify as much as possible
a. [latex]\frac{3ax^2}{4b}\ \times\ \frac{6b^2}{27x^2y}[/latex]
b. [latex]\frac{{(x-2y)}^2}{x^2-5xy+6y^2}\ \times\ \frac{x+2y}{x^2-4xy+4y^2}[/latex]
c. [latex]\frac{4x^2-8x-5}{4x-4}\ \times\ \frac{x-1}{4x^2-25}[/latex]
2. Divide the following rational expressions and simplify as much as possible
a. [latex]\frac{6x^2-7x-3}{x^2-1}\ \div\ \frac{2x-3}{x-1}[/latex]
b. [latex]\frac{x^2+5x+6}{x^2-2x-3}\ \div\ \frac{4x+12}{x-3}[/latex]
c. [latex]\frac{x^2-8x+15}{x^2-9x+14}\div\frac{x^2+4x-21}{x-1}[/latex]
d. [latex]\frac{{15x}^2+11x+2}{5x+15}\ \div\ \frac{{3x}^2-20x-7}{x+3}[/latex]