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 01-21-2009 #1 (permalink) Sexy Bish <3   Join Date: Jun 2008 Location: █♣█ Posts: 2,437 iTrader: (22) Math: Grade 11 Advanced Functions (3U) - Rational Expressions Having extreme difficulty with these questions. Help? 1. Simplify. (x + 2)² (x - 1)² - (x - 4)² (x + 4)² 2. Simplify and state any restrictions. a) Code: a+b a-b 2a+b ___ - ______ - ____ a ab + b² b __________________ Last edited by SkillzKillz; 01-21-2009 at 08:14 PM.
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 01-21-2009 #2 (permalink) killing threda since 2007   Join Date: Aug 2008 Posts: 793 Blog Entries: 5 iTrader: (2) IGN: fLick3r/MrsT/Cod Class: Bow/Saw/Cannon Level: 111/58/58 Guild: Moogles #1: Take the second part, its easier. (x-4)²(x+4)²= [(x-4)(x+4)]², much easier that way - you'll get a binomial squared. For the first part, i'd do [(x+2)(x-1)]²=(x²+x-2)² then i'd just crank a trinomial squared, it's like foil except you have more combinations (9 combinations). Spoiler! 1. ... = (x²+x-2)²-[(x-4)(x+4)]² ...= (x^4+x^3 -2x^2 +x^3 + x^2-2x+-2x^2 - 2x+ 4) - [x^2-16]² ...= (x^4 + 2x^3 -3x^2-4x+4) - (x^4-32x^2+256) ...=(2x^3-35x^2-4x+260) or something like that. 2. Find the common denominator: should be a²b+ab²... gives you (a+b)(ab+b²)-(a-b)(a)-(2a+b)(a²+b) all over (a²b+ab²) simplifying the numerator gives you the answer in simplified form, you might be able to factor out and cancel the a's and b's after that. For the restrictions, you look at the denominators for the original problem: we can't divide by 0 (impossible!) so none of the denominators can equal 0. ... In other words (<> means "does not equal"), a<>0, ab+b^2 <> 0, and b <> 0. solving the second equation gives b(a+b) <> 0, a+b <>0 a<>-b __________________ if the post above this is insightful/useful, rep me plz --------------------------- fLick3r(main)/Cod(92%PvP)/Secretary(PvE)
 11-10-2011 #3 (permalink) Banned   Join Date: Nov 2011 Posts: 4 iTrader: (0) I was wondering, in this question to simplifying rational expressions ?? Find (-6x^2 - 4xy + 8x)/(2x) do they want me to find out what the variables are, or do they want me to do something else with it? That is the exact way they have the question written down.
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 Originally Posted by geeknick I was wondering, in this question to simplifying rational expressions ?? Find (-6x^2 - 4xy + 8x)/(2x) do they want me to find out what the variables are, or do they want me to do something else with it? That is the exact way they have the question written down.
When they say to simplify, take it literally -- "make it simpler." They don't need you to solve for any variables since they don't have an equal sign for it to add up to. The way I'd tackle this is to see if there's anything they all have in common.

In the numerator, you see that all the coefficients are even, so off-the-bat you can factor out a 2. Then you see that they also have an "x" in common, so factor out a 2x int he numerator. That should get you to:

Quote:
 [ 2x (-3x - 2y + 4) ] / [ 2x ]
Notice that you have a 2x in the numerator and the denominator. Because it's a fraction, you can go ahead and cancel these out because you're dividing that out. That'll get you to a final answer of:

Quote:
 -3x + 2y + 4
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Quote:
 Originally Posted by kuyaBaka When they say to simplify, take it literally -- "make it simpler." They don't need you to solve for any variables since they don't have an equal sign for it to add up to. The way I'd tackle this is to see if there's anything they all have in common. In the numerator, you see that all the coefficients are even, so off-the-bat you can factor out a 2. Then you see that they also have an "x" in common, so factor out a 2x int he numerator. That should get you to: Notice that you have a 2x in the numerator and the denominator. Because it's a fraction, you can go ahead and cancel these out because you're dividing that out. That'll get you to a final answer of:

Thanks a Bunch for the help,..........

 11-14-2011 #6 (permalink) Banned   Join Date: Nov 2011 Posts: 4 iTrader: (0) The Fastest Way To Solve Addition Of Fractions Through Vedic Math, TRIX FOR THE SAT Take these fractions for example 1/2 +1/3 how do u add them fast well first we need to cross multiply 1*3=3 1*2=2 u get the numbers three and two now simply take the to answers and do the following 3+2 ____ 3*2 5/6 there u go u get the answer and u can use this for any addition of fractions -------------------- ---- hope this helps NICK

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