Rational Expressions

Simplify Rational Expressions

R U Rational r Irrational?

And How Do U Know?

​Dr. Tom Giles

Multiple Choice

Simplify 

• $$\frac{n-9}{n+9}$$  

• $$\frac{1}{x-9}$$  

• $$x+9$$  

• $$\frac{1}{x+9}$$  

Multiple Choice

$$Simplify:\ \frac{5a^3c^{10}}{20a^5c^4}$$  

• $$\frac{4c^6}{a^2}$$  

• $$\frac{1a^2c^6}{4}$$  

• $$\frac{1c^6}{4a^2}$$  

• $$\frac{1a^2}{4c^6}$$  

Multiple Choice

$$Simplify:\ \ \frac{x^2+7x+12}{x^2+4x}$$  

• $$\frac{x+3}{x+4}$$  

• $$\frac{x-3}{x}$$  

• $$\frac{x+3}{x}$$  

• $$\frac{x+3}{x^2}$$  

Multiple Choice

Simplify
$$\frac{x^2+6x+8}{x^2-x-6}$$  

• $$\frac{x+2}{x-3}$$  

• $$\frac{x+4}{x+2}$$  

• $$\frac{x+4}{x-3}$$  

• $$\frac{x+2}{x-2}$$  

Multiple Choice

Simplify

$$\frac{15x^2}{5x^3}$$  

• $$3x$$  

• $$\frac{3}{x}$$  

• $$\frac{x}{3}$$  

• $$\frac{5}{x}$$  

Multiple Choice

Simplify

$$\frac{8x+32}{x+4}$$  

• $$\frac{8}{x-4}$$  

• $$\frac{-x}{x-4}$$  

• $$-8$$  

• $$8$$  

Multiple Choice

$$Simplify:\ \ \frac{x^2+6x-7}{x^2-49}$$  

• $$\frac{x-1}{x+7}$$  

• $$\frac{x+1}{x+7}$$  

• $$\frac{x-1}{x-7}$$  

• $$\frac{x+1}{x-7}$$  

Multiple Choice

$$Simplify:\ \ \frac{x^2+6x}{x^2+3x-18}$$  

• $$\frac{x}{x+3}$$  

• $$\frac{x}{x-3}$$  

• $$\frac{x+6}{x-3}$$  

• $$\frac{x}{x+6}$$  

Multiple Choice

$$Simplify:\ \ \frac{x^2+7x+10}{x^2-4}$$  

• $$\frac{x-5}{x+2}$$  

• $$\frac{x-5}{x-2}$$  

• $$\frac{x+5}{x+2}$$  

• $$\frac{x+5}{x-2}$$  

Multiple Choice

$$Simplify:\ \ \frac{x^2-25}{x^2-6x+5}$$  

• $$\frac{x+5}{x-1}$$  

• $$\frac{x-5}{x-1}$$  

• $$\frac{x+5}{x+1}$$  

• $$\frac{x-5}{x+1}$$  

Multiple Choice

Simply the rational expression.

• 2a²b⁶

• 1/2a²b⁶

• b⁶/2a²

• 2b⁶/a²

Multiple Choice

Simplify

• (x-9)/(x+9)
• 1/(x-9)
• (x+9)
• 1/(x+9)

Multiple Choice

Multiply and Simplify

• (n-10)/8n+56
• (n-10)(n+7)/8n+56
• (n-10)/8
• (n+10)/8

Multiple Choice

Divide and Simplify

• A
• B
• C
• D

Multiple Choice

Simplify and state the excluded values.

• A
• B
• C
• D

Multiple Choice

Simplify $$\frac{7n}{3n-18}+\frac{n+3}{3}$$  

• $$\frac{8n+3}{3n-15}$$  

• $$\frac{n^2+4n-18}{3\left(n-6\right)}$$  

• $$\frac{7\left(n+3\right)}{3\left(3n-18\right)}$$  

• $$\frac{7n+n+3}{3n-18+3}$$  

Multiple Choice

Simplify $$\frac{8n}{n-3}+\frac{3n}{5n-6}$$  

• $$\frac{43n^2-9}{\left(5n-6\right)\left(n-3\right)}$$  

• $$\frac{11n}{6n-9}$$  

• $$\frac{43n^2-57n}{\left(n-3\right)\left(5n-6\right)}$$  

• $$\frac{8n+3n}{n-3+5n-6}$$  

Multiple Choice

$$\frac{m^2+m-30}{m^2+13m\ +42}\div\frac{m-2}{m+7}$$  Simplify

• $$\frac{m-5}{m-2}$$  

• $$\frac{\left(m-5\right)\left(m-2\right)}{\left(m+7\right)^2}$$  

• $$\frac{m^2+2m-32}{m^2+14m+49}$$  

• $$\frac{-5}{2m^2}$$  

Multiple Choice

$$\frac{2}{8m^3-64m^2}\div\frac{1}{8m^2}$$  

• $$\frac{2}{m-64m^2}$$  

• $$\frac{16m^2}{8m^2\left(m-8\right)}$$  

• $$\frac{2}{64m^4\left(m-8\right)}$$  

• $$\frac{2}{m-8}$$  

Multiple Choice

Multiply the Rational Expression

• A

• B

• C

• D

Multiple Choice

Simplify: 

$$\frac{8x}{x-4}-\frac{11}{3x+1}$$  

• $$\frac{24x^2-3x-44}{\left(3x+1\right)\left(x-4\right)}$$  

• $$\frac{24x^2+19x-44}{\left(3x+1\right)\left(x-4\right)}$$  

• $$\frac{24x^2-3x+44}{\left(3x+1\right)\left(x-4\right)}$$  

• $$\frac{13x^2+52x}{\left(3x+1\right)\left(x-4\right)}$$  

Multiple Choice

Simplify: 

$$\frac{6}{2x+3}-\frac{8}{x-1}$$  

• $$\frac{-10x+18}{\left(x-1\right)\left(2x+3\right)}$$  

• $$\frac{-10x-30}{\left(x-1\right)\left(2x+3\right)}$$  

• $$\frac{22x+18}{\left(x-1\right)\left(2x+3\right)}$$  

• $$\frac{22x+30}{\left(x-1\right)\left(2x+3\right)}$$  

Multiple Choice

Perform the operation

• A
• B
• C
• D

Multiple Choice

Perform the operation

• A
• B
• C
• D

Multiple Choice

Subtract

$$\frac{6}{x^2+4x-32}-\frac{x-5}{x-4}$$  

• $$\frac{-x^2+3x-34}{\left(x+8\right)\left(x-4\right)}\ ,\ x\ne-8,\ 4$$  

• $$\frac{-x^2+3x-34}{\left(x+8\right)\left(x-4\right)}\ ,\ x\ne-4,\ 8$$  

• $$\frac{-x^2-3x+46}{\left(x+8\right)\left(x-4\right)}\ ,\ x\ne-8,\ 4$$  

• $$\frac{-x^2-3x+46}{\left(x+8\right)\left(x-4\right)}\ ,\ x\ne-4,\ 8$$  

Multiple Choice

• A.4x³/(x+2)
• B.4x³/(x+10)
• C.2x³/(5x+1)
• D. 2x³/(x+5)

Multiple Choice

Simplify

• A
• B
• C
• D

Multiple Choice

Divide and Simplify

• A
• B
• C
• D

Multiple Choice

• A

• B

• C

• D

• E

Multiple Choice

• A

• B

• C

• D

Multiple Choice

• A

• B

• C

• D