For the past two weeks, we’ve been learning about rational expressions. we’ve learned to add and subtract, multiply and divide. today ill be showing you how to multiply and divide because I personally think it’s the funniest. you get to go around and cross things out when they cancel and you don’t have to find a common denominator.

example:
\frac{(x^2-4)(2+4x)}{(x+2)(x+5)}\cdot\frac{(2x^2+5)(x+5)}{(x^2-4)(2+4x)}

notice how all expressions are in brackets when two sets of brackets are beside each other like (x+x)(y+y) they are very easy to pull apart, they have a very weak bond.

(note: when canceling you can only go from top to bottom not side to side)

both sides of the dot have the following in common:
(x+5)(x^2-4)(2+4x)

\frac{(x^2-4)(2+4x)}{(x+2)(x+5)}\cdot\frac{(2x^2+5)(x+5)}{(x^2-4)(2+4x)} -> \frac{2x^2+5}{x+2}

once canceling all the like terms your answer is \frac{2x^2+5}{x+2} now you look to see if there are any smaller like terms to simplify further but there are none.

the finale step is to place your domain restriction x\neq-2,2,5

adding/subtractings bond:

multiplying/dividings bond:

Unit 6 Summary Assignment

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