Show your solution. Evaluate each rational expression using the indicated values for the variable. 1. 2x2 3 a.) x = -2 b.) x = 3 2. a2 b2 a.) a = 6, 9 = 3 b.) a = -5, b = 10 3. 3x x-3 a.) x = 5 b.) x = -4 4. c-5 2d+23 a.) c = 4, d = 2 b.) c = 10, d = 6 5. 3e 5-f2 a.) e = -2, f = 3 b.) e = 4, f = -1​

1. SOLUTION:a) x = -2[tex]\begin{aligned} \frac{2x^2}{3} & = \frac{2(-2)^2}{3} \\ & = \frac{2(4)}{3} \\ & = \boxed{\frac{8}{3}} \end{aligned}[/tex]b) x = 3[tex]\begin{aligned} \frac{2x^2}{3} & = \frac{2(3)^2}{3} \\ & = \frac{2(9)}{3} \\ & = \frac{18}{3} \\ & = \boxed{6} \end{aligned}[/tex]2. SOLUTION:a) a = 6, b = 3[tex]\begin{aligned} \frac{a^2}{b^2} & = \frac{6^2}{3^2} \\ & = \frac{36}{9} \\ & = \boxed{4} \end{aligned}[/tex]b) a = -5, b = 10[tex]\begin{aligned} \frac{a^2}{b^2} & = \frac{(-5)^2}{10^2} \\ & = \frac{25}{100} \\ & = \boxed{\frac{1}{4}} \end{aligned}[/tex]3. SOLUTION:a) x = 5[tex]\begin{aligned} \frac{3x}{x - 3} & = \frac{3(5)}{5 - 3} \\ & = \boxed{\frac{15}{2}} \end{aligned}[/tex]b) x = -4[tex]\begin{aligned} \frac{3x}{x - 3} & = \frac{3(-4)}{-4 - 3} \\ & = \frac{-12}{-7} \\ & = \boxed{\frac{12}{7}} \end{aligned}[/tex]4. SOLUTION:a) c = 4, d = 2[tex]\begin{aligned} \frac{c - 5}{2d + 23} & = \frac{4 - 5}{2(2) + 23} \\ & = \frac{-1}{4 + 23} \\ & = \boxed{-\frac{1}{27}} \end{aligned}[/tex]b) c = 10, d = 6[tex]\begin{aligned} \frac{c - 5}{2d + 23} & = \frac{10 - 5}{2(6) + 23} \\ & = \frac{5}{12 + 23} \\ & = \frac{5}{35} \\ & = \boxed{\frac{1}{7}} \end{aligned}[/tex]5. SOLUTION:a) e = -2, f = 3[tex]\begin{aligned} \frac{3e}{5 - f^2} & = \frac{3(-2)}{5 - 3^2} \\ & = \frac{-6}{5 - 9} \\ & = \frac{-6}{-4} \\ & = \boxed{\frac{3}{2}} \end{aligned}[/tex]b) e = 4, f = -1[tex]\begin{aligned} \frac{3e}{5 - f^2} & = \frac{3(4)}{5 - (-1)^2} \\ & = \frac{12}{5 - 1} \\ & = \frac{12}{4} \\ & = \boxed{3} \end{aligned}[/tex]

Answered by GreatRedSpot | 2024-09-09