Simplify the expression. (This type of expression arises in calculus when using the "quotient rule.")$$\frac{2(1+x)^{1 / 2}-x(1+x)^{-1 / 2}}{x+1}$$
Explain why possible solutions must be checked in radical equations.
Explain why $|2 x+5|=-7$ has no solutions.
For the following exercises, solve the rational exponent equation. Use factoring where necessary.$$x^{\frac{2}{3}}=16$$
For the following exercises, solve the rational exponent equation. Use factoring where necessary.$$2 x^{2}-x^{\frac{1}{4}}=0$$
For the following exercises, solve the rational exponent equation. Use factoring where necessary.$$(x+1)^{\frac{2}{3}}=4$$