Rational expression

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Rational expression

  1. 1. RATIONAL EXPRESSION by : DR. T.K. JAIN AFTERSCHO ☺ OL centre for social entrepreneurship sivakamu veterinary hospital road bikaner 334001 rajasthan, india FOR – PGPSE / CSE PARTICIPANTS mobile : 91+9414430763
  2. 2. My words.... Here I present a few basic questions on rational expression I wish that more people should become entrepreneurs. An ordinary Indian entrepreneur wishes to remain an honest entrepreneur and contribute to the development of nation but we have to strengthen those institutions which truly promote entrepreneurship, not just degree granting institutions. Let us work together to promote knowledge, wisdom, social development and education. We believe in free education for all, free support for all, entrepreneurship opportunities and training for all. Let us work together for these goals. ... I alone cant do much, I need support of perosns like you .......... ...
  3. 3. What is the degree of this polynomial : 3x^4+2x^3+5x^2 +12x+7 Answer: = it is a polynomial of degree 4 (the highest exponent (power) that X has is 4. )
  4. 4. What is additive inverse of p(x) / q(x) Answer = -p(x) / q(x)
  5. 5. What should be added to 2x^2+x+3 to get 12x^2-12x -88 ? p(x) = (12x^2-12x -88) - (2x^2+x+3) =10x^2 -13x-91 answer
  6. 6. What should be subtracted from 2x^2+11x+3 to get 6x^2-32x -8 ? p(x) = (2x^2+11x+3) - ( 6x^2-32x -8) = -4x^2+43x+11 answer
  7. 7. What is the value of : ((x/y-1)/(1-x/y)) ((x/y-1)/(1-x/y)) can be written as : ((x-y)/y)/(y-x)/y)) we can write it as : ((x-y)/y) * (Y /(y-x))) multiply -1 to y-x to get x-y, now we get -1 as answer =-1 answer
  8. 8. What is the simplied form of : (x^3 – 27) / ( x^2+3x +9) We can write it as : ((x-3)( x^2+3x +9) ) /( x^2+3x +9) we get : (x-3) or x = 3 answer
  9. 9. What is the simplied form of : (x^3 –64) / ( x^2+4x +16) We can write it as : ((x-4)( x^2+4x +16) ) /( x^2+4x +16) we get : (x-4) or x =4 answer
  10. 10. X = a/ (a+b) and Y = b / (a-b), what is 1/x + 1/y ? We can write it as : (a+b) / a + (a-b) / b lcm is ab (b(a+b) + a(a-b) ) / ab (ab+b^2 +a^2-ab ) / ab =(a^2 + b^2) / ab answer
  11. 11. X = 1/ (a-b) and Y = 1 / (a+b), what is 1/x + 1/y ? We can write it as : (a+b) + (a-b) = 2a answer
  12. 12. Which of these are correct ? a. every rational expression is a polynominal b. every polynomial is a rational expression answer : (both the statements are correct).
  13. 13. Simplify it : (x^2-7x+12)/(x^2-4x+3) * (x^2 -11x+28)/ (x^2-8x+7) We can write it as : ((x-3) (x-4))/ ((x-1)(x-3) * (x-4) (x – 7)/ (x-7) (x -1) (x-3)*(x-4)(x-4)((x-7) / ((x-1)(x-3)(x-7)(x-1) we can cancel out (x-3), (x-7) (x^2 -8x +16) / (x^2 -2x +1) answer
  14. 14. Simplify it : (x^2-5x+6)/(x^2-9x+20) * (x^2 -5x+4)/ (x^2-3x+2) We can write it as : ((x-3) (x-2))/ ((x-4)(x-5) * (x-4) (x – 1)/ (x-2) (x -1) (x-3)*(x-2)(x-4)((x-1) / ((x-4)(x-5)(x-2)(x-1) we can cancel out (x-3), (x-1) ,(x-4) =(x-3) / (x-5) answer
  15. 15. Simplify : (x^2 +8x+12) / (x^2 +4x -12) We can write it as ((x+2)(x+6)) / ( (x-2)(x+6)) we can cancel (x+6) we get =(x+2) / (x -2) answer
  16. 16. Simplify it : (( 1+1/(x+1)) (1+(1/(x+2)) (1 + 1/(x+3))(( 1+1/(x+4))(( 1+1/(x+5)) We can write it as : ((x+2)/(x+1)) ((x+3)/(x+2))((x+4)/(x+3))((x+5)/(x+4))((x+6)/(x+5)) we can cancel the similar terms, we get : = (x+6) / (x+1) answer
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  20. 20. 2^(2x-1) = 1/(8^(x-3)), what is x? Options : 3,2,0,-2 put x = 2 and you get the answer
  21. 21. 3^(4x-2) = 729, what is x? Options : 1,1.5,2,2.5, try to put the value x=2, you get the answer
  22. 22. 32^1/3 = 2^x, what is x? Options : 5,3,3/5,5/3 answer :
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  25. 25. Spread the concepts of AFTERSCHOOOL Join PGPSE start CENTRES of AFTERSCHOOOL spread entrepreneurship & social entrepreneurship let us work for social upliftment together let us work for some common goals conduct workshops on social entrepreneurship make your career in social entrepreneurship
  26. 26. THANKS.... GIVE YOUR SUGGESTIONS AND JOIN AFTERSCHOOOL NETWORK / START AFTERSCHOOOL SOCIAL ENTREPRENEURSHIP NETWORK IN YOUR CITY / COLLEGE [email_address] PGPSE – WORLD'S MOST COMPREHENSIVE PROGRAMME IN SOCIAL ENTREPRENEURSHIP

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