Problems

1. Find all excluded values for the following expressions.

   (a). $\dfrac{10}{8-2w}$

   (b). $\dfrac{8t-7}{15+3t}$

2. Find all excluded values for the following expressions.

   (a). $\dfrac{2x+7}{x^2+2x-35}$

   (b). $\dfrac{u+4}{u^2-64}$

3. The function $g$ is defined as follows.

   $g(x) = \dfrac{x-7}{x^2+10x+16}$

   Find $g(-5)$

4. The function $h$ is defined as follows.

   $h(x)=\dfrac{x^2-5x-36}{x^2-16x+64}$

   Find $h(8)$

5. The function $f$ is defined below.

   $f(x)=\dfrac{x+4}{x^2-1}$

   Find all the values of $x$ that are NOT in the domain of $f$.

6. The function $g$ is defined below.

   $g(x)=\dfrac{2x-9}{x^2-18x+81}$

   Find all values of $x$ that are NOT in the domain of $g$.

7. Simplify.

   (a). $\dfrac{35(5x+7)(x-6)^2}{28(x-6)(5x+7)^4}$

   (b). $\dfrac{27w^2(w+5)^5}{18w^4(w+5)^4(3w+7)}$

8. Simplify.

   (a). $\dfrac{12y^2-28y}{4y^2-20y}$

   (b). $\dfrac{3w+12}{7w^2+28w}$

9. For each expression, simplify if possible.

   (a). $\dfrac{6-5y}{5y-6}$

   (b). $\dfrac{2x+3}{3x+2}$

   (c). $\dfrac{-8+w}{w-8}$

Answer key

1. (a). $w=4$

   (b). $t=-5$

2. (a). $x=-7, 5$

   (b). $u=8, -8$

3. $\dfrac{4}{3}$

4. Undefined.

5. $x=1, -1$

6. $x=9$

7. (a). $\dfrac{5(x-6)}{4(5x+7)^3}$

   (b). $\dfrac{3(w+5)}{2w^2(3w+7)}$

8. (a). $\dfrac{3y-7}{y-5}$

   (b). $\dfrac{3}{7w}$

9. (a). $-1$

   (b). Cannot be simplified.

   (c). $1$