Write each of the following rational expressions as a single quotient of two polynomials in standard form. You can check your answer by testing the initial expression and your result at some simple values of the variables to ensure they’re equal.
\(\displaystyle \frac{3x}{x+1}-\frac{x-1}{2x} \)
\(\displaystyle \frac{x-3}{10x} + \frac{x+7}{5x^3} \)
\(\displaystyle \frac{t-1}{t+1} - \frac{t}{1+t} \)
\(\displaystyle \frac{y}{2x} + 3\frac{x+1}{x^2y} \)
\(\displaystyle \frac{z}{5x-1} + \frac{z+y}{2y} \)
\(\displaystyle \frac{1}{x} + \frac{1}{y} + \frac{1}{z} \)
\(\displaystyle \frac{x+z}{x} + \frac{y}{y+z} + \frac{y}{x} \)
\(\displaystyle \frac{3t}{\sqrt{t}} + \frac{\sqrt{t}-1}{t} \)
\(\displaystyle \frac{z}{\tfrac{x}{y}} + \frac{\tfrac{x}{y}}{z} \)
\(\displaystyle \frac{\frac{x}{y}-\frac{y}{x}}{x} + \frac{y}{\frac{x}{y}+\frac{y}{x}}\)
\(\displaystyle \frac{1}{1+\frac{1}{1+\frac{1}{x}}} \)
\(\displaystyle \frac{\frac{\frac{x+1}{x}+1}{x}+1}{x} \)