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How To simplify Rational expressions By Factoring
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Feb 20, 2025
Today’s lesson was very straight forward, we worked on simplifying rational expressions using factoring. We three different cases we were presented with and each one required a specific method. I hope this video helps If you need help in math, be sure to check out http://tayibs.com/get-math-help/
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you
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so in this section we are basically
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simplifying rational expression correct
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and then we work for number one number
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two and number three and each case was
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different all right
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so number one without taking one of
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attack so for x squared over two x plus
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three years and you're told
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simplify the rational expression
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expression each possible so I'm gonna
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lay it out and even gonna separate the
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numerator which we did here for explain
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it one spirit that's four times X times
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X and then the denominator just works or
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query across three X so now we just come
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on factor Y X right here and if you pull
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out it X out of the whoops well you left
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with 2x and if you brought the X out of
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the three you left with three 3x right
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so it's X parenthesis 2x plus 3 and now
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you rewrite the expression ask 4 times X
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times X over x times 2x plus 3 and then
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now you can simplify the like terms
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which is the axon the axon your left
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foot forward so what 2x plus 3 right yes
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now the next one was this one here x
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squared minus 2x minus 15 about x
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squared minus 4x minus 5 remember we
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work on this like last year how to
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factor this kind of second-degree
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equations so now we want to product with
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some whose two numbers whose product is
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negative 15 and so I'm is negative two
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right and good on the corner here we
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have three and five 3 times 5 is 15
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now how do we work on this number so
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that if song gives you negative two is
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what we're looking for
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so negative three plus five gives you
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positive - that's not gonna work for
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negative 5 plus 3 is negative two so
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that works so we go back and we rewrite
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the expression as X minus 5 in the X
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plus three that's what the numerator
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and for the denominator we'll repeat the
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same steps you want two numbers whose
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product is negative five and so is
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negative four and you immediately found
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5 and 1 and 5 minus 1 is 4 negative 5
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plus 1 is negative 4 so that's the bet
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better digits so we go back and we do
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the same thing we replace it and then we
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regret the whole expression that's the X
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minus 5 X plus 3 X minus 5 X plus 1 and
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then we can select it like terms and we
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are left with this and the last part we
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experiment 16 over x squared plus X
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minus 12 and this is different this is
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the pitar the difference of two perfect
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squares so we recall the formula a
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square minus B Square a minus B and if
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we're gonna apply that here if X square
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minus 16 so that will give you X minus 4
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and X plus 4 then we take that and we
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work on it the denominator we did the
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same stuff that we did previously we
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broke down the denominator and we want
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two numbers whose product is negative 2
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where the Sun was one was 4 negative 3
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we rewrite the whole thing and then we
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go ahead and simplify the expressions ok
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easy enough right here and now you're
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gonna work on your own you know