8/26 Unit 1 Review - Rational Expressions (2 of 2)

8/26 Unit 1 Review

Rational Expressions (2 of 2)

​Math Analysis HON

by Ms. Kunkel

​You will need to know how to..

• ​Simplify Rational Expressions

• ​Multiply Rational Expressions

• ​Divide Complex Rational Expressions

• ​Add and Subtract Rational Expressions

​Simplifying Rational Expressions

• ​Factor Completely

• ​Cancel out any matches in the numerator and denominator

• ​Remember when dividing with exponents you subtract them.

• ​You can only simplify if its being multiplied, unless you can divide the same thing out of ALL terms.

• ​The denominator cannot = 0 so whatever values would make the denominator 0 is excluded from the domain

Home

Open in new tab

Copy link

Multiple Choice

Reduce, or simplify

the rational expression.

• 3 x y³

• 8 x³ y

• 3 x³ y

• 8 x y³

Multiple Choice

Reduce, or simplify

the algebraic fraction.

• x - 3

• -21

• -3

• ( x - 3 ) / ( x )

Multiple Choice

Reduce, or simplify

the rational expression.

• ( x + 5 )( x - 5 ) / ( x + 5 )( x - 2 )

• ( x - 5 ) / ( x - 2 )

• ( x + 5 ) / ( x - 2 )

• -25 / ( 3x - 10 )

​Multiplying Rational Expressions

• ​Multiply straight across.

• ​Factor everything and cross off common factors in the numerator and denominator

Home

Open in new tab

Copy link

Multiple Choice

Multiply and Simplify

• 4(x+3)/(x+2),

• (x+2)/4(x+1)

• (x+2)/4(x+3),

• 4(x+1)/(x+2),

Multiple Choice

  $$\frac{3b^2-6b}{b^2+2b-3}\cdot\frac{b^2-8b+7}{b-2}$$  

• $$\frac{1}{b\left(b-2\right)};\ b\ne0,\ 2$$  

• $$\frac{b-3}{3b^2\left(b+6\right)};\ b\ne-6,\ 0$$  

• $$b-8;\ b\ =\ all\ real\ numbers$$  

• $$\frac{3b\left(b-7\right)}{b+3};\ b\ \ne-3,\ 1,\ 2$$  

Multiple Choice

$$\frac{24+5x-x^2}{x^2-5x-24}\cdot\frac{8x+24}{7x^2+21x}$$  

• $$7;\ x\ =\ all\ real\ numbers$$  

• $$\frac{x+5}{3x};\ x\ne0$$  

• $$21x;\ x\ =\ all\ real\ numbers$$  

• $$-\frac{8}{7x};\ x\ne-3,\ 0,\ 8$$  

​Dividing Complex Rational Expressions

• ​If it is complex fraction (fraction on top of another fraction) rewrite it our horizontally

• ​KEEP CHANGE FLIP!!

• ​Then follow rules for multiplication

Home

Open in new tab

Copy link

Multiple Choice

Divide and Simplify

• 1/6

• x+10/ 6x+60

• x+8/ 6x+60 

• (x+10)(x+8)/ 6x+60

Multiple Choice

Divide the Rational Expression

• A

• B

• C

• D

Multiple Choice

Simplify: $$\frac{\frac{5k^3-25k^2}{5k^2}}{\frac{k^2+2k-35}{9}}$$  

• $$\frac{4k^2}{k-7}$$  

• $$\frac{9}{k+7}$$  

• $$\frac{9}{4}$$  

• 1

​Adding and Subtracting Rational Expression

• ​You must have a common denominator.

• ​Whatever you multiply the bottom by, you must also multiply to the top

• ​Remember when subtracting you must change ALL the signs in the numerator of the second fraction

Home

Open in new tab

Copy link

Multiple Choice

Simplify the expression.

Multiple Choice

Add

• A.

• B.

• C.

• D.

Multiple Choice

Subtract: $$\frac{5x-3}{x+2}-\frac{3x-1}{x+2}$$  

• $$\frac{2x-4}{x+2}$$  

• $$\frac{8x-4}{x+2}$$  

• $$\frac{2x-2}{x+2}$$  

• $$\frac{2x-2}{0}$$  

Multiple Choice

Add: $$\frac{5}{x-2}+\frac{3}{x+7}$$  

• $$\frac{8}{\left(x-2\right)\left(x+7\right)}$$  

• $$\frac{8}{2x+5}$$  

• $$\frac{8x}{\left(x-2\right)\left(x+7\right)}$$  

• $$\frac{8x+29}{\left(x-2\right)\left(x+7\right)}$$  

​The End!

​Make sure to study Part 1 - Factoring