EJERCICIOS DE ALGEBRA. efectúe las operaciones indicadas y simplifique.

Del libro Jagdish C. Arya, y Robin W. Lardner. (2009). Matemáticas aplicadas a la administración y a la economía, 5ª ed., México, Prentice-Hall, resuelve los ejercicios presentados en las páginas 53 y 54.

(1-40) En las expresiones siguientes, efectúe las operaciones indicadas y simplifique.

1.- 4x/(2x+3)+6/(2x+3) = 4x6/(2x+3) = (2(2x+3))/(2x+3)= 2

2.- 2x/(x-2)-4/(x-2) = (2x-4)/(x-2) = (2(x-2))/(x-2)= 2

3.- x^2/(x-3)-(5x-6)/(x-3) =(x^2-5x+6)/(x-3) = =((x-2)(x-3))/(x-3) = x-2

4.- (2-3x)/(x-1)+x^2/(x-1) =〖2-3x+x〗^2/(x-1) = =((x-2)(x-1))/(x-1) = x-2

5.- (2x-1)/(x-2)+3 =〖2x-1+3(x+2)〗^ /(x-2) = 〖2x+1+3x+6〗^ /(x-2) =〖5x+7〗^ /(x-2)

6.- (3x-2)/(x+1)-2 =〖3x-2-2(x+1)〗^ /(x+1) = 〖3x-2-2x-2〗^ /(x+1) =〖x-4〗^ /(x+1)

7.- x/(x+2)+3/(2x-1) = (x(2x-1)+3(x+2))/((x+2)(2x-1)) = (〖2x〗^2-x+3x+6)/(〖2x〗^2-x+4x-2)= (〖2x〗^2+2x+6)/(〖2x〗^2+3x-2)

8.- x/(2x-6)+(x-2)/(x+1) = (x(x+1)+(2x-6)(x-2))/((2x-6)(x+1)) = (x^2+x+〖2x〗^2-4x-6x+12)/(〖2x〗^2-x+4x-2)= (〖3x〗^2-9x+12)/(〖2x〗^2+3x-2)

9.- 2/(x-1)-(3x+1)/(x+1) = (2(x+1)-(3x+1)(x-1))/((x-1)(x+1)) = (〖2x+2-3x〗^2+3x-x+1)/((x-1)(x+1))= (〖-3x〗^2+4x+3)/((x-1)(x+1))

10.- x/(2x+3)-(2x-3)/(4x+1) = (x(4x+1)-(2x+3)(2x-3))/((2x+3)(4x+1)) = (〖4x〗^2+x-〖4x〗^2+6x-6x+9)/((2x+3)(4x+1))= (x+9)/((2x+3)(4x+1))

11.- 2x/(2x-1)-(x+2)/(x+1) = (2x(x+1)-(2x-1)(x+2))/((2x-1)(x+1)) = (〖2x〗^2+2x-〖2x〗^2-4x+x+2)/((2x-1)(x+1))= (-x+2)/((2x-1)(x+1))

12.- 2/(5x-6)-4/(10x-2) = (2(10x-2)-4(5x-6))/((5x-6)(10x-2)) = (〖20x-4-〗^ 20x+24)/((5x-6)2(5x-2))= 20/(2(x-1)(x+1))=10/((5x-6)(5x-2))

13.- 1/(x^2-5x+6)-1/(x^2-3x+2) =1/((x-3)(x-2))-1/((x-1)(x-2))=((x-1)(x-2)-(x-3)(x-2))/((x-3)(x-2)(x-1)(x-2))=((x-1)-(x-3))/((x-3)(x-2)(x-1))=2/((x-3)(x-2)(x-1))

14.- x/(x^2+2x-3)+1/(x^2+x-2) =x/((x+3)(x-1))+1/((x-1)(x+2))=(x(x+2)+(x+3))/((x+3)(x-1)(x+2))=(x^2+2x+x+3)/((x+3)(x+2)(x-1))=(x^2+3x+3)/((x+3)(x+2)(x-1))

15.- x/(x^2+2x-3)+1/(1-2x+x^2 ) =x/((x+3)(x-1))-1/〖(x-1)〗^2 =(x(x-1)+(x+3))/((x+3)〖(x-1)〗^2 )=(x^2-x+x+3))/((x+3)〖(x-1)〗^2 )=(x^2+3)/((x+3)〖(x-1)〗^2 )

16.- 2/(〖9x〗^2+6x+1)-3/(x+1)+1/(〖3x〗^2+2x-1)=1/〖(3x-1)〗^2 -3/(x+1)+1/((3x-1)(x+1))=((x+1)-3(3x-1)^2+(3x-1))/〖(x+1)(3x-1)〗^2 = =(3(〖9x〗^2+6x+1)+x+3x+1-1)/〖(x+1)(3x-1)〗^2 = (27x^2+18x+3+4x)/〖(x+1)(3x-1)〗^2 = (27x^2+22x+3)/〖(x+1)(3x-1)〗^2

17.- 1/(x^2+4x+3)+3/(x^2-1)-2/(x+3)=1/((x+1)(x+3))+3/((x+1)(x-1))-2/(x+3)=((x-1)+3(x+3)-2(x+1)(x-1))/((x+1)(x+3)(x-1))=(x-1+3x+9-2x^2+2))/((x+1)(x+3)(x-1))= =(-2x^2+4x+10)/((x+1)(x+3)(x-1))

18.- 2/(2x^2-x-1)+3/(1-2x+x^2 )+2=2/(2x^2-x-1)+3/〖(x-1)〗^2 +2=2/(2x^2-x-1)+3/〖(x-1)〗^2 +(2〖(x-1)〗^2)/〖(x-1)〗^2

=(2〖(x-1)〗^2+3(2x^2-x-1)+2(2x^2-x-1)〖(x-1)〗^2)/((2x^2-x-1)〖(x-1)〗^2 )=(2〖x^2-4x+2〗^ +6x^2-3x-3+(4x^2-2x-2)〖(x-1)〗^2)/((2x^2-x-1)〖(x-1)〗^2 )= (2〖x^2-4x+2〗^ +6x^2-3x-3+4x^4-12x^3+4x^2-2x^3+4x^2-2x-2x^2+4x-2)/((2x^2-x-1)〖(x-1)〗^2 )= (4x^4-12x^3+18x^2-10x-3)/((2x^2-x-1)〖(x-1)〗^2 )=

19.- ((x^2-1)/x)((x^2+2x)/(x+1))= .- (((x-1)(x+1))/x)((x(x+2))/(x+1))= ((x-1)(x+1)x(x+2))/(x(x+1))=(x-1)(x+2)

20.- ((x^2+4x)/(2x+6))((2x+4)/(x+4))= ((x(x+4))/(2(x+3)))((2(x+2))/(x+4))=(x(x+4)2(x+2))/(2(x+3)(x+4))=(x(x+2))/(x+3)

21.- (2x+4)/(1-x)*(x^2-1)/(3x+6)=(2(x+2)(x^2-1))/((1-x)3(x+2))=(2(x-1)(x+1))/3(1-x) =((-1)2(x-1)(x+1))/((-1)3(1-x) )=(-2(x-1)(x+1))/3(x-1) =(-2(x+1))/3

22.- (x^2-7x+12)/(x^2-x-2)*(x^2+4x+3)/(2x^2-5x-3)=((x-3)(x-4)(x+1)(x+3))/((x-2)(x+1)(x-3)(2x+1))=((x-4)(x+3))/((x-2)(2x+1))

23.- ((x^2+5x+6)/(x^2-6x+8))((〖2x〗^2+9x+4)/(〖2x〗^2+7x+3))=((x+2)(x+3)(2x+1)(x+4))/((x-2)(x-4)(2x+1)(x+3))=((x+2)(x+4))/((x-2)(x-4))

24.- ((〖2x〗^4-2x)/(〖2x〗^2-5x-3))((〖2x〗^2-3x-2)/(x^3+x^2+x))=((x^2+x+1)(x-1)2x(x-2)(2x+1))/(x-3)(2x+1)x(x^2+x+1) =(2(x-1)(x-2))/((x-3) )

25.- (3+1/(x-1))(1-1/(3x-2))=((3(x-1))/(x-1)+1/(x-1))((3x-2)/(3x-2)-1/(3x-2))=((3(x-1)+1)/(x-1))((3x-2-1)/(3x-2))=((3x-3+1)/(x-1))((3x-2-1)/(3x-2)) = ((3x-2)/(x-1))((3x-3)/(3x-2))=((3x-2)3(x-1))/((x-1)(3x-2))=3

26.- (x-3/(x-2))(9/(x^2-9)-1)=.- ((x(x-2))/(x-2)-3/(x-2))(9/(x^2-9)-(x^2-9)/(x^2-9))=((x^2-2x-3)/(x-2))(x^2/(x^2-9))=(((x-3)(x+1))/(x-2))(x^2/((x-3)(x+3))) =

(x^2 (x+1))/((x-2)(x+3))

27.- ((x^2+x)/(2x+1))÷((x^3-x)/(4x+2))= ((x(x+1))/(2x+1))÷((〖x(x〗^2-1))/(2(2x+1)))=(x(x+1)2(2x+1))/((2x+1) 〖x(x〗^2-1))=(2(x+1))/(〖(x〗^2-1))

28.- ((3x-6)/(〖2x〗^2+4x+2))÷((x^2-4)/(x^2+3x+2))=((3(x-2))/〖2(x+1)〗^2 )÷(((x-2)(x+2))/((x+1)(x+2)))=(3(x-2)(x+1))/(〖2(x+1)〗^2 (x-2))=3/〖2(x+1)〗^

29.- (〖3x〗^2-x-2)/(x^2-x-2)÷(3x^2+5x+2)/(2x^2-5x+2)=((x-1)(3x+2))/((x-2)(x+1))÷((3x+2)(x+1))/((x-2)(2x-1))=((x-1)(3x+2)(x-2)(2x-1))/((x-2)(x+1)(3x+2)(x+1))=((x-1)(2x-1))/〖(x+1)〗^2

30.- (〖2x〗^2+x-1)/(2x^2+10x+12)÷〖1-4x〗^2/(4x^2+8x-12)=((2x-1)(x+1))/(2(x+2)(x+3))÷((-2x+1)(2x+1))/(4(x-1)(x+3))=((2x-1)(x+1)4(x-1)(x+3))/(2(x+2)(x+3)(-2x+1)(2x+1))=(2(x+1)(x-1))/((x+2)(-2x+1))

31.-

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