Domain of Rational Expressions

​P6. Rational Expressions

Multiple Choice

What is an excluded value? #1

• A value that makes the denominator equal to 0

• A number that makes the numerator equal to 0

• The solution

• An ostracized number

Multiple Choice

The domain of the rational expression is: $$\frac{\left(x-11\right)\left(x+12\right)}{\left(x-10\right)\left(x+2\right)}$$  #2

• all real numbers except: -10, 2

• all real numbers except: -11, 12

• cannot be found

• all real numbers except: 10, -2

Multiple Choice

Determine the excluded values. #3

• x = 0, 3

• x = 0, -3

• x = 0, -3, 5

• x = 0, 3, 5

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Multiple Choice

Simplify

$$\frac{12x^2-54x}{6x}\cdot\frac{6}{81-18x}$$  #7

• $$-\frac{2}{3}$$  

• $$-1$$  

• $$\frac{x-7}{5x^2}$$  

• $$\frac{x-4}{6}$$  

Multiple Choice

Multiply the expressions. $$\frac{\left(n-1\right)\left(n-5\right)}{2\left(n+3\right)}\cdot\frac{2\left(n+3\right)}{n-5}$$  

#8

• $$n-1$$  

• $$\frac{2\left(n-1\right)}{n+3}$$  

• $$2\left(n-1\right)$$  

• $$1$$  

Multiple Choice

Simplify

$$\frac{x^2-49}{20x^3}\cdot\frac{4x^2-24x}{x^2+x-42}$$  #11

• $$-\frac{2}{3}$$  

• $$-1$$  

• $$\frac{x-7}{5x^2}$$  

• $$\frac{x-4}{6}$$  

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Multiple Choice

Divide the expression  $$\frac{x+8}{6\left(x+10\right)}\div\frac{\left(x+8\right)\left(x-8\right)}{\left(x+10\right)\left(x-8\right)}$$  #14

• $$\frac{1}{6}$$  

• $$\frac{\left(x+10\right)}{6x+60}$$  

• $$\frac{x+8}{6x+60}$$  

• $$\frac{\left(x+10\right)\left(x+8\right)}{6x+60}$$  

Multiple Choice

Divide

$$\frac{x^2+10x+21}{x^2-9}\div\frac{x+7}{x-7}$$  #15

• $$\frac{x-10}{x-3}$$  

• $$\frac{10x+7}{3}$$  

• $$\frac{x+3}{x-7}$$  

• $$\frac{x-7}{x-3}$$  

Multiple Choice

Divide the rational expression.

$$\frac{6}{k-4}\div\frac{k+6}{k^2+2k-24}$$  #16

• $$\frac{9}{k-4}$$  

• $$\frac{k+7}{8}$$  

• $$6$$  

• $$k-3$$  

Multiple Choice

Add $$\frac{2x-3}{4x-7}+\frac{2x-3}{4x-7}$$  #25

• $$\frac{4x-6}{4x-7}\ ,\ x\ne-\frac{7}{4}$$  

• $$\frac{4x^2-6x+9}{4x-7}\ ,\ \ x\ne\frac{7}{4}$$  

• $$\frac{4x-6}{4x-7\ }\ ,\ x\ne\frac{7}{4}$$

• $$\frac{4x-6}{8x-14},\ x\ne\frac{14}{8}$$  

Multiple Select

What might you have to do to add/subtract rational expressions? #22

• Make sure you have a common denominator and keep only one of them!

• Change signs on some of the terms if you are subtracting!

• Simplify the numerator.

• Keep Change Flip

Multiple Choice

Add the expressions. $$\frac{2x}{x^2-36}+\frac{x+4}{x+6}$$  #26

• $$\frac{x^2-24}{\left(x+6\right)\left(x-6\right)}\ ,\ x\ne\pm6$$  

• $$\frac{x^3+6x^2-24x}{\left(x^2-36\right)\left(x+6\right)}\ x\ne-6,\ 36$$  

• $$\frac{x^2+2x-24}{\left(x+6\right)\left(x-6\right)}\ ,\ x\ne\pm6$$  

• $$\frac{x^2+12x+24}{\left(x+6\right)\left(x-6\right)}\ ,\ x\ne\pm6$$  

Multiple Choice

Add $$\frac{3x-2}{x+2}+\frac{2x}{4x-1}$$  #27

• $$\frac{14x^2-7x+2}{\left(x+2\right)\left(4x-1\right)};\ x\ne-2,\ \frac{1}{4}$$  

• $$\frac{14x^2-9x-2}{\left(x+2\right)\left(4x-1\right)};\ x\ne-2,\ 1$$  

• $$\frac{12x^2-7x+2}{\left(x+2\right)\left(4x-1\right)};\ x\ne-2,\ \frac{1}{4}$$  

• $$\frac{14x^2-7x+2}{\left(x+2\right)\left(4x-1\right)};\ x\ne-\frac{1}{4},\ 2$$  

Multiple Choice

Simplify the expression. #29

• n / 2m

• n / 3m

• (m² + 4n²) / 12m

• n / 4m

Multiple Choice

#31

Multiple Choice

Perform the indicated operation and simplify: $$\frac{x^2+5x-34}{x^2-9x+8}-\frac{10}{x-8}$$  #36

• $$\frac{x^2-5x-44}{\left(x-8\right)\left(x-1\right)}$$  

• $$\frac{x^2-5x-24}{\left(x-8\right)\left(x-1\right)}$$  

• $$\frac{x+6}{x-1}$$  

• $$\frac{x+3}{x-1}$$  

Multiple Choice

Find the sum/difference. Give your answer in the simplest form. #37

•   $$\frac{p-2}{p+5}$$  

•   $$\frac{p+2}{p+5}$$  

•   $$\frac{p-2}{p-5}$$  

Multiple Choice

Simplify: $$\frac{\frac{1}{x}-\frac{1}{y}}{\frac{1}{x}+\frac{1}{y}}$$  #38

• $$\frac{y-x}{y+x}$$  

• $$\frac{y+x}{y-x}$$  

• $$\frac{y}{y-x}$$  

• $$\frac{1}{y+x}$$  

Multiple Choice

Simplify:  $$\frac{\frac{x}{5}}{\frac{4}{x+6}}$$  #42

• $$\frac{4x}{5\left(x+6\right)}$$  

• $$20x\left(x+6\right)$$  

• $$\frac{x\left(x+6\right)}{20}$$  

• $$\frac{x+6}{20x}$$  

Multiple Choice

simplify: $$\frac{\frac{x}{25}+\frac{x}{5}}{\frac{5}{x}}$$  #41

• $$\frac{25x^2}{400+4x}$$  

• $$\frac{6x^2}{125}$$  

• $$\frac{400x}{x^3-16}$$  

• $$\frac{x^2+x^3}{625}$$