Answer Key 8.1

Terrance Berg

Answer Key 8.1

$\frac{4 (4) + 2}{6} \Rightarrow \frac{16 + 2}{6} \Rightarrow \frac{18}{6} \Rightarrow 3$
$\frac{- 2 - 3}{3 (- 2) - 9} \Rightarrow \frac{- 5}{- 6 - 9} \Rightarrow \frac{- 5}{- 15} \Rightarrow \frac{1}{3}$
$\frac{- 4 - 3}{(- 4)^{2} - 4 (- 4) + 3} \Rightarrow \frac{- 7}{16 + 16 + 3} \Rightarrow - \frac{7}{35} \Rightarrow - \frac{1}{5}$
$\frac{- 1 + 2}{(- 1)^{2} + 3 (- 1) + 2} \Rightarrow \frac{1}{1 - 3 + 2} \Rightarrow \frac{1}{0} \Rightarrow Undefined$
$\frac{b + 2}{b^{2} + 4 b + 4} \Rightarrow \frac{2}{4} \Rightarrow \frac{1}{2}$
$\frac{(4)^{2} - 4 - 6}{4 - 3} \Rightarrow \frac{16 - 10}{1} \Rightarrow \frac{6}{1} \Rightarrow 6$
$\begin{array}{rrrrr} k & + & 10 & \neq & 0 \\ - & 10 & - 10 \\ k & \neq & - 10 \end{array}$
$\begin{array}{rrrrr} 18 p (p & - & 2) \\ 18 p & \neq & 0 \\ p & \neq & 0 \\ p & - & 2 & \neq & 0 \\ + & 2 & + 2 \\ p & \neq & 2 \end{array}$
$\begin{array}{rrr} 10 m & \neq & 0 \\ m & \neq & 0 \end{array}$
$2 (3 x + 10) \Rightarrow \begin{array}{rrrrr} 3 x & + & 10 & \neq & 0 \\ - & 10 & - 10 \\ 3 x & \neq & - 10 \\ x & \neq & - \frac{10}{3} \end{array}$
$\begin{array}{rrr} 5 (r & + & 2) \\ r & \neq & - 2 \end{array}$
$\begin{array}{rrr} 3 n (2 n & + & 1) \\ n & \neq & 0 \\ n & \neq & - \frac{1}{2} \end{array}$
$\begin{array}{rrr} (b - 4) (b + 8) \\ b & \neq & 4 \\ b & \neq & - 8 \end{array}$
$\begin{array}{rrr} 5 v (7 v & - & 1) \\ v & \neq & 0 \\ v & \neq & \frac{1}{7} \end{array}$
$\frac{21 x^{2}}{18 x} \Rightarrow \frac{3 \cdot 7 \cdot x \cdot x}{3 \cdot 6 \cdot x} \Rightarrow \frac{7 x}{6}$
$\frac{12 n}{4 n^{2}} \Rightarrow \frac{3 \cdot 4 \cdot n}{4 \cdot n \cdot n} \Rightarrow \frac{3}{n}$
$\frac{24 a}{40 a^{2}} \Rightarrow \frac{3 \cdot 8 \cdot a}{5 \cdot 8 \cdot a \cdot a} \Rightarrow \frac{3}{5 a}$
$\frac{21 k}{24 k^{2}} \Rightarrow \frac{3 \cdot 7 \cdot k}{3 \cdot 8 \cdot k} \Rightarrow \frac{7}{8 k}$
$\frac{18 m - 24}{60} \Rightarrow \frac{6 (3 m - 4)}{6 (10)} \Rightarrow \frac{3 m - 4}{10}$
$\frac{n - 9}{9 n - 81} \Rightarrow \frac{n - 9}{9 (n - 9)} \Rightarrow \frac{1}{9}$
$\frac{x + 1}{x^{2} + 8 x + 7} \Rightarrow \frac{x + 1}{(x + 1) (x + 7)} \Rightarrow \frac{1}{x + 7}$
$\frac{28 m + 12}{36} \Rightarrow \frac{4 (7 m + 3)}{4 (9)} \Rightarrow \frac{7 m + 3}{9}$
$\frac{n^{2} + 4 n - 12}{n^{2} - 7 n + 10} \Rightarrow \frac{(n + 6) (n - 2)}{(n - 5) (n - 2)} \Rightarrow \frac{n + 6}{n - 5}$
$\frac{b^{2} + 14 b + 48}{b^{2} + 15 b + 56} \Rightarrow \frac{(b + 8) (b + 6)}{(b + 8) (b + 7)} \Rightarrow \frac{b + 6}{b + 7}$
$\frac{9 v + 54}{v^{2} - 4 v - 60} \Rightarrow \frac{9 (v - 6)}{(v - 10) (v + 6)} \Rightarrow \frac{9}{v - 10}$
$\frac{k^{2} - 12 k + 32}{k^{2} - 64} \Rightarrow \frac{(k - 8) (k - 4)}{(k - 8) (k + 8)} \Rightarrow \frac{k - 4}{k + 8}$
$\frac{2 n^{2} + 19 n - 10}{9 n + 90} \Rightarrow \frac{(2 n - 1) (n + 10)}{9 (n + 10)} \Rightarrow \frac{2 n - 1}{9}$
$\frac{3 x^{2} - 29 x + 40}{5 x^{2} - 30 x - 80} \Rightarrow \frac{(3 x - 5) (x - 8)}{5 (x + 2) (x - 8)} \Rightarrow \frac{3 x - 5}{5 (x + 2)}$
$\frac{2 x^{2} - 10 x + 8}{3 x^{2} - 7 x + 4} \Rightarrow \frac{2 (x - 4) (x - 1)}{(3 x - 4) (x - 1)} \Rightarrow \frac{2 (x - 4)}{3 x - 4}$
$\frac{7 n^{2} - 32 n + 16}{4 n - 16} \Rightarrow \frac{(7 n - 4) (n - 4)}{4 (n - 4)} \Rightarrow \frac{7 n - 4}{4}$
$\frac{7 a^{2} - 26 a - 45}{6 a^{2} - 34 a + 20} \Rightarrow \frac{(a - 5) (7 a + 9)}{2 (3 a - 2) (a - 5)} \Rightarrow \frac{7 a + 9}{2 (3 a - 2)}$
$\frac{4 k^{3} - 2 k^{2} - 2 k}{k^{3} - 18 k^{2} + 9 k} \Rightarrow \frac{2 k (2 k^{2} - k - 1)}{k (k^{2} - 18 k + 9)} \Rightarrow \frac{2 (2 k^{2} - k - 1)}{k^{2} - 18 k + 9}$

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Intermediate Algebra (Convert to MathJax) Copyright © 2020 by Terrance Berg is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.

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