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. 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. 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. )
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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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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