Rational Expressions (2 of 2)

Rational Expressions

​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

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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

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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

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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

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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: $$\frac{5}{x-2}+\frac{3}{x+7}$$  

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

• $$\frac{8}{2x+5}$$  

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

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

Fill in the Blank

Simplify: $$\frac{5}{2x}+\frac{3}{x}-\frac{9}{4x}$$  

​The End!