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• Rational expressions
• Operations with Rational Expressions
• Reducing Rational Expressions

# Reducing Rational Expressions

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•  Question 1: 1 pts Determine the value of the variable for which the rational expression is not defined. $$\dfrac{60x^{3}}{12x}$$
 $x = 0$ $x = 30$ $x=3$ $x=12$
•  Question 2: 1 pts $$-\dfrac{x-2}{x-3}=\dfrac{2-x}{x-3}$$
•  Question 3: 1 pts $$\dfrac{z-5}{7-z}=\dfrac{5-z}{7-z}$$
•  Question 4: 1 pts Simplify expression. $$\dfrac{32n^{2}}{24n}$$
 $\dfrac{3n}{2}$ $\dfrac{2n}{3}$ $\dfrac{3n}{4}$ $\dfrac{4n}{3}$
•  Question 5: 2 pts Simplify expression. $$\dfrac{15a-3}{24}$$
 $\dfrac{3a-1}{8}$ $\dfrac{4a-1}{2}$ $\dfrac{5a-1}{8}$ $\dfrac{5a-1}{6}$
•  Question 6: 2 pts Simplify expression. $$\dfrac{x^{2}-16}{x-4}$$
 $x+2$ $x-2$ $x-4$ $x+4$
•  Question 7: 2 pts Simplify the expression. $$\dfrac{j+8}{j^{2}-64}$$
 $\dfrac{1}{j+8}$ $\dfrac{1}{j-8}$ $\dfrac{1}{8-j}$ $\dfrac{8-j}{1}$
•  Question 8: 2 pts Simplify the expression. $$\dfrac{4n-4}{6n-20}$$
 $\dfrac{2 \cdot (n-1)}{3n-10}$ $\dfrac{ n-1}{3n-10}$ $\dfrac{ (n-1)}{2 \cdot (3n-10)}$ $\dfrac{ 2n-1}{ 3n-10}$
•  Question 9: 3 pts Simplify expression. $$\dfrac{x^{3}-x^{2}-42x}{2x^{2}-20x+42}$$
 $\dfrac{ 3 \cdot(x-6)}{2 \cdot (x-3)}$ $\dfrac{ x \cdot(x-6)}{2 \cdot (x+3)}$ $\dfrac{ x \cdot(x+6)}{2 \cdot (x-3)}$ $\dfrac{ x \cdot(x-6)}{2 \cdot (x-3)}$
•  Question 10: 3 pts Which values of $y$ make the expression undefined? $$\dfrac{3y^{2}-39y+90}{y^{2}-3y-70}$$
 $y = -7$ and $y=10$ $y = 7$ and $y=10$ $y = -7$ and $y=-10$ $y = -7$ and $y=-10$
•  Question 11: 3 pts Simplify the expression. $$\dfrac{k^{2}-y^{2}}{3k+3y}$$
•  Question 12: 1 pts The domain of the rational expression $$\frac{5x}{2x^{2}+8}$$ is all $x.$