Solve the rational equation. If the equation has no solution, so state. \( x^{2}+x-20 \) \( +\frac{1}{x^{2}+6 x+5}=\frac{5}{x^{2}-3 x-4} \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice A. The solution set is \( \} \). (Simplify your answer. Use a comma to separate answers as needed.) B. There are infinitely many solutions. C. There is no solution.

Solve the equation by factoring. Select the correct solution. \( 6 x^{2}-5 x-4=0 \) \( \begin{array}{ll}\text { O } & \text { A) } x=-\frac{4}{3},-\frac{1}{2} \\ \text { O } & \text { B) } x=-\frac{1}{2}, \frac{4}{3} \\ \text { O } & \text { C) } x=-\frac{4}{3}, \frac{1}{2} \\ \text { - } & \text { D) } x=\frac{1}{2}, \frac{4}{3}\end{array} \)

Consider the line \( y=\frac{5}{2} x-3 \). Find the equation of the line that is perpendicular to this line and passes through the point \( (2,-5) \). Find the equation of the line that is parallel to this line and passes through the point (2, -5). Note that the ALEKS graphing calculator may be helpful in checking your answer. Equation of perpendicular line:

Write in exponential form. \[ \log _{6} 216=3 \] Write the equivalent exponential equation. \( \square \) (Type an equation. Type your answer using expc

1. Louls owns his own orchard. He plants 5 fruit trees for every 5 nut tiees. The equation \( f=\frac{9}{5} n \) models the relationship between the number of nut trees planted and the number of fruit trees planted. Determine the number of nut trees planted if 135 fruit trees were planted.

Use the properties of logarithms to rewrite the expression. Simplify the res \( \log _{3} \frac{\sqrt{x} \sqrt[3]{y}}{w} \sqrt{z} \) Choose the correct answer. A. \( -\frac{1}{2} \log _{3} x-\frac{1}{3} \log _{3} y+5 \log _{3} w+\frac{1}{2} \log _{3} z \) B. \( \frac{1}{2} \log _{3} x+\frac{1}{3} \log _{3} y-5 \log _{3} w-\frac{1}{2} \log _{3} z \) C. \( { }^{2} \log _{3} x+3 \log _{3} y-5 \log _{3} w-2 \log _{3} z \) D. This cannot be simplified.