11.4 Homework Problems: Complex Fractions
1. Simplify the complex fraction
a. [latex]\frac{\frac{2x}{3y^2}}{\frac{5x^2}{6y}}[/latex]
b. [latex]\frac{\frac{x+3}{2x}}{\frac{2x-1}{4x^2}}[/latex]
c. [latex]\frac{\frac{2x-1}{x}}{\frac{2}{x}+3}[/latex]
d. [latex]\frac{\frac{1}{3}+\frac{1}{x}}{\frac{1}{2}-\frac{1}{x}}[/latex]
e. [latex]\frac{\frac{4}{x}-1}{1-\frac{1}{x-3}}[/latex]
f. [latex]\frac{\frac{1}{x+h}-\frac{1}{x}}{h}[/latex]
g. [latex]\frac{\frac{x+1}{x-1}-\frac{x-1}{x+{1}}}{\frac{x+1}{x-1}+\frac{x-1}{x+1}}[/latex]
h. [latex]\frac{\frac{x}{x-4}-\frac{1}{x-1}}{\frac{x}{x-1}+\frac{2}{x-3}}[/latex]
i. [latex]\frac{1}{x+1}-\frac{3}{2x}\cdot\frac{4x}{x+1}[/latex]
j. [latex]\frac{x}{x-1}-\frac{3}{x-1}\cdot\frac{x+2}{x}[/latex]
k. [latex]\frac{\frac{1}{y+t}-\frac{1}{t}}{y}[/latex]
l. [latex]\frac{\frac{3y^2}{y+5}}{\frac{12y^4}{y^2+10y+25}}[/latex]