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Transcript of Project 9.2
* * Rational Expressions By Kiran Sharma What is a Rational Expression? A rational expression consists of fractions
that has a numerator and or denominator
that are polynomials. Dawkins, Paul. "Pauls Online Notes: Algebra-Rational Expressions." lamar.edu. N.p. n.d. Web. 17 May 2011. Basic Operations Multiply Divide Subtract Add Simplify Simplifying This is the first step that needs to be mastered in order to become good at applying other operations on rational expressions and equations. Factoring is utilized in simplifying rational expressions Difference of Squares/Cubes
Shortcut The 3 main types of factoring: Basically, an expression
containing fractions. In order to simplify a problem, one must follow these 3 steps: 1) Factor the numerator
2) Factor the denominator
3) Cancel out repeating factors When simplifying a fraction like this one, you can reduce the numbers out front (the 3 and 9) because they are not factors. 3x^2+6x 9x+18 3x(x+2) 9(x+2) Use GCF factoring on top and bottom Cancel the common factor 3x(x+2) 9(x+2) GCF Simplified answer: 1x 3 Always check to see if you can factor any part of the expression first! Difference of Squares & Shortcut Addition & Subtraction Just like how you would add and subtract with regular, basic fraction problems, one must get like denominators to complete these operations with rational expressions as well. x^2+4x-5 x^2-1 Factor the numerator using the shortcut method (x+5)(x-1) x^2-1 Now, factor the bottom by difference of squares (x+1)(x-1) (x+5)(x-1) Divide out common factor (x+5)(x-1) (x+1)(x-1) Cannot simplify further (x+5) (x+1) LCD lowest common denominator However, whenever you add or subtract fractions, you have to find the LCD of the 2 unklike denominators first in order to simplify the problem Rational Expressions Rational Equations vs Do not have an equals sign Do have an equals sign Both types contain fractions You simplify these You solve these Incomplete statement Complete mathematical statement If there is a variable, solve for that variable "Solving Rational Equations." tutor-homework.com.N.p. n.d. Web. 19 May 2011. <http://www.tutor-homework.com/Math_Help/college_algebra/m3l2notes1.pdf>. The same methods of simplifying that were shown earlier are used to help simplify these addition and subtraction problems While following these steps, do not forget to do things like distributing a negative and combining like terms! ************* ************* + . . 7x x-4 Distribute the negative sign! (4x+12) x-4 - 7x-4x-12 These basic skills still apply! x-4 Combine like terms in the numerator 3x-12 x-4 Use GCF factoring on the top 3(x-4) x-4 Cancel out common factor Answer= 3 Example with like denominators To find the LCD of 2 denominators, you use the same 3 steps as we did earlier with simplifying: 1) Number
3) Factor Example of finding LCD The 2 denominators: 21x^2 3x^2-15x & Use GCF factoring on the 2nd one 21x^2 & 3x(x-5) 1) Ask what the closest number is that both numbers can multiply to Answer: 21 2) Ask yourself what is the common variable both go into Answer: x^2 3) Ask if there is a factor Answer: (x-5) LCD: 21x^2(x-5) Multiplying & Dividing Example with unlike denominators 6 4x^2 + 2 5x what you multiply the bottom by you
must do the same to the top 30 Multiply to get like denominators 20x^2 + 8x 20x^2 Reduce by dividing
everything by 2 15+4x 10x^2 Applications Applications Applications Applications Applications Applications Applications Motion problems You do not need common denominators when multiplying and dividing! ******************* ******************* ******************* ******************* Multiplication Division x-3 2x-8 * 6x^2-96 x^2-9 Factor where needed x-3 2(x-4) * 6(x^2-16) (x+3)(x-3) Cancel out common factors
and use difference of squares on top x-3 2(x-4) * 6(x+4)(x-4) (x+3)(x-3) Write what is left 6(x+4) 2(x+3) Reduce 3(x+4) x+3 x^2-14x+48 x^2-6x / . . (3x-24) Factor, multiply by the reciprocal,
and cancel out common factors (x-8)(x-6) x(x-6) * 1 3(x-8) Answer: 1 3x d= r x t r= d/t Making a workout plan This involves simplifying Figuring out someone's burn rate of calories This uses addition and subtraction "Cartoon Car Picture." freeonlinepicture.org. N.p. n.d. Web. 20 May 2011. <http://www.freeonlinepicture.org/tag/cartoon-car-picture/>. "Excercise=Happiness." fitnesstogetherorlandpark.com. N.p. n.d. Web. 20 May 2011. <http://fitnesstogetherorlandpark.com/tag/fitness-together/page/2/>. Doctor's use when prescribing dosages Farmers use them when harvesting You can use these expressions to figure
out how much gas you will use on a trip and the driving time Can figure out how much money you make at a summer job depending on the hours