12.1 Homework Problems: Solving Rational Equations
1. State any restrictions on x, then solve the rational equations for x
a. [latex]\frac{4x}{7}=\frac{x+5}{3}[/latex]
b. [latex]\frac{4}{x-4}=\frac{2}{x+3}[/latex]
c. [latex]\frac{5x+2}{x-6}=\frac{11}{4}[/latex]
d. [latex]\frac{2}{x^{2\ }-9}=\ \frac{1}{x^2}+\ \frac{1}{x^2-3x}[/latex]
e. [latex]\frac{5x}{4}-\frac{1}{2}=-\frac{3}{16}[/latex]
f. [latex]\frac{x-2}{3}-\frac{x-3}{5}=\frac{13}{15}[/latex]
g. [latex]\frac{2}{4x-1}+\frac{1}{x+1}=\frac{3}{x+1}[/latex]
h. [latex]\frac{3x+5}{3x+2}+\frac{8x+16}{3x^2-4x-4}=\frac{x+2}{x-2}[/latex]
i. [latex]\frac{x-2}{x-3}+\frac{x-3}{x-2}=\frac{2x^2}{x^2-5x+6}[/latex]
j. [latex]\frac{3}{3x-1}+\frac{1}{x+1}=\ \frac{4}{2x-1}[/latex]