Ecuaciones

Simplificación de fracciones algebraicas

(40x^2 y^3 c)/(48x^3 y^2 z)= (2∙2∙2∙5 xx yyy c)/(2∙2∙2∙2∙3 xxx yy z)=5yc/6xz=5cy/6xz

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

(x^2+2x+1)/(x^2+5x+4)=((x+1)(x+1))/((x+4)(x+1))=(x+1)/(x+4)

(nx+ny+mx+my)/(n^2-m^2 )=((nx+ny)(mx+my))/((n-m)(n+m))=(n(x+y)m(x+y))/((n-m)(n+m))=((n-m)(x+4))/((n-m)(n+m))=(x+y)/(n-m)

(x^2+x-20)/(x^2-25)=((x+5)(x-4))/(x^2-25)=((x+5)(x-4))/((x+5)(x-5))=(x-4)/(x-5)

(2a-4b)/(12b-6a)=(2(a-2b))/(6a-12b)=2/6=1/3

(x^3-8)/(x^2-4)=((x-2)(x^2+2x+4))/((x-2)(x+2))=(x^2+2x+4)/(x+2)

(a^2-a-20)/(a^2+a-30)=((a+4)(a-5))/((a-5)(a+6))=(a+4)/(a+6)

(x^3+27)/(x^2-3x+9)=((x+3)(x^2-3x+9))/((x^2-3x+9)(1))=(x+3)/1=x+3

(ax-ay)/(x^2-y^2 )=(a(x-y))/((x+y)(x-y))=a/(x+y)

(x^2-a)/(12a-4ax)=((x+3)(x-3))/(4a(3-x))=(x+3)/4a

(x^2-7x+10)/(x^3-125)=((x-5)(x-2))/((x-5)(x^2+5x+25))=(x-2)/(x^2+5x+25)=(x-2)/((x+5)(x+5))

(x^2-2x-3)/(ax+a)=((x-3)(x+1))/(a(x+1))=(x-3)/a

(x^2+2x-3)/(x^2-3x-18)=((x+3)(x-1))/((x-6)(x+3))=(x-1)/(x-6)

(x^3+64)/(5x+20)=((x+4)(x^2-4x+16))/(5(x+4))=(x^2-4x+16)/5=((x-4)(x-4))/5

(3 x^2-16x+5)/(x^2-ax+20)=((3x-1)(x-5))/((x-5)(x-4))=(3x-1)/(x-4)

(x^2+5x)/(x^2+10x+25)=(x(x+5))/(x+5)(x+5) =x/(x+5)

(2x^2-11x+14)/(4x^2-4a)=((2x-7)(x-2))/((2x+7)(2x-7))=(x-2)/(2x+7)

(2x+4)/(x+4)∙(x^2-y^2)/(4x+8)=(2x+4)(x^2-y^2 )/(x+4)(4x+8) =(x+2)(x+y)(x-y)/(x+4)4(x+2) =((x+y)(x-y))/(2(x+4))

(m^3+m^2 n)/(mn-m^2 )∙(m^3-m^2 n)/(m^3 n+m^4 )=(m^2 (m+n) m^2 (m-n))/(m(n-m) m^3 (n+m) )=m^4/m^2 =1

(y^2+8y+15)/(y^2-25)∙(4y-20)/(y^2-3y)=(y+5)(y+3)y(y-5)/(y+5)(y-5)y(y-3) =(y(y+3))/(y(y-3))

(7a+7b)/(14a^2 )∙(a^2-ab)/(a^2-b^2 )=7(a+b)a(a-b)/(7∙2∙a∙a(a-b)(a+b) )=1/2a

(y^3+y^2)/(y^2-1)∙(〖4y〗^2-4y)/y^3 =y(y^2+y)2y(2y-2)/((y+1)(y-1) y^3 )=y(y+1)2(y-1)/(y+1)(y-1) =2y

(y^2-ay+20)/(25-y^2 )∙(y^2-5y)/(y^2-4y)=(y-5)(y-4)y(y-5)/(5+y)(5-y)y(y-4) =(y-5)/(5+y)

(x^3+64)/(x^2-16)∙(6x-24)/(x^3-4x^2+16x)=(x+4)(x^2-4x+16)6(x-4)/(x-4)(x+4) =〖(x〗^2-4x+16)6=6(x-4)(x-4)

(x^2+3x-bx-3b)/(x^2-b^2 )∙(nx+nb)/(4x+12)=(〖(x〗^2 bx)(3x-3b)n(x+b))/(x+b)(x-b)4(x+3) =(x(x+b)+3(x-b)n)/(x-b)4(x+3) =(x+3)(x-b)n/((x-b)4(x+3))

(x^2-9)/(2x^2+2x)∙(4x-4)/(x^2+2x-3)∙(x+1)/(x-3)=(x+3)(x-3)4(x-1)(x+1)/2x(x+1)(x+3)(x-1)(x-3) =2/x

(5x^2+13x-6)/(4-25x^2 )∙(10x+4)/(9-x^2 )=(5x^2+13x-6-2(5x+2))/((2-5x)(2+5x)(3-x)(3+x))

Diferencia de cuadrados

(2y-14)/(y^2-2y-35)÷(6y-30)/(y^2-25)=(2(y-7)(y+5)(y-5))/((y-7)(y+5)6(y-5))=2/6=1/3

(9x-27)/(15x-30)÷(6x^2-18x)/(7x-14) (9(x-3)7(x-2))/(15(x-2)6x(x-3))=7/10x

(x^2+7x+10)/(x^2-5x)÷(x^2-4)/2x=(x+5)(x+2)2x/(x(x+5)(x+2)(x-2))=2/(x-2)

(a^2-6a+8)/(a^2-4a)÷(4-a^2)/2a=(a-4)(a-2)2a/(a(a-4)(a+2)(a-2))=2/(a+2)

(b^2-2b-8)/(4b-b^2 )÷(4-b^2)/(5b-10)=((b+2)(b-4)5(b-2))/(b(4-b)(2-b)(2+b))=5/b

(x^3+8)/(x^2-14)÷(x^3-2x^2+4x)/(2a-ax)=((x+2)(x^2-2x+4)a(2-x))/((x^2-14)x(x^2-2x+4))=((x+2)a(2-x))/(x^2-14)x

(x^2-4x-21)/(x^3+27)÷(7x-x^2)/(x^3 y-3x^3+9xy)=((x-7)(x+3)x(x^2 y-3x+9y))/((x+3)(x^2-3x+9)x(x-7))=(x^2 y-3x+9y)/(x^2-3x+9)

(n^2-a)/(n^3-27)÷(2n^3+6n^2)/(n^3+3n^2+an)=((n+3)(n-3)n(n^2+3n+a))/((n-3)(n^2+3n+a)2n(n+3))=1/2n

(3x^2+11x-20)/(8x-40)÷(7x^2-16)/(6x+8)=((3x-4)(x+5)2(3x+4))/(8(x-5)(3x+4)(-3x-4))=(2(x+5))/(8(x-5))=(x+5)/(4x-5)

(7a^2+7a+6)/(a^2-4)÷(6-14a)/(2a^2+8a+8)=((7a+6)(a+1))/((a-2)(a+2)2(3-7a))

1.-

2x/(x^2-16)+8/(x^2-16)=x^2-16=(x+4)(x-4) m.c.m.(x+4)(x-4)

x^2-16=(x+4)(x-4)

2.- ((x+4)(x-4))/((x+4)(x-4))+((x+4)(x-4))/((x+4)(x-4))=1+1

3.- ((1)(2x)+(1)(8))/((x+4)(x-4))=(2x+8)/((x+4)(x-4)) 4.- (2(x+4))/((x+4)(x-4))=2/(x-4)

6n/(n-5)-30/(n-5)=n-5 (n-5)/(n-5)-(n-5)/(n-5)=1-1

(1(6n)-(30)(-1))/(n-5)=(6n+30)/(n-5)

(9b-5)/(b-1)-(7b-3)/(b-1)=(b-1) (b-1)/(b-1)-(b-1)/(b-1)=1-1

((1)(9b-5)-(7b-3)(1))/(b-1)=(9b-5-7b-3)/(b-1)=(2b-8)/(b-1)=(2(b-4))/(b-1)

10/(a-5)+2a/(5-a)=a-5 (a-5)/(a-5) (a-5)/(5-a)=1+1

((1)(10)+(29)(1))/(a-5)=(10+29)/(a-5)=39/(a-5)

ax/(x-y)-ay/(x-y)=(x-4)(x-y) (x-4)(x-y)/(x-4)-(x-4)(x-4)/(x-y)=

3/5x-8/3x=(5x)(3x)=15x^2 (5x)(3x)/5x=(5x)(3x)/3x=3x-5x

((3x)(3)-(8)(5x))/((5x)(3x))=(ax+40x)/(15x^2 )=49x/(15x^2 )=(49(x))/(15x(x))=4a/15x

(2y-5)/7+(y-2)/2=2.7 2.7/7+2.7/2=2+7 (4y+10+7y-14)/14 (11y-24)/14

(4x-3)/8-(2x-7)/4=2^3=8 8/8-8/4=1-2 ((1)(4x-3)-(2x-7)(-2))/8=(4x-3+4x-14)/8=(8x-17)/8

7/x+2/(x+2)=(x)(x+2) ((x)(x+2))/x+((x)(x+2))/(x+2)=(x+2)(x)

((x+2)(7)+(2)(x))/((x+2)(x))=((7x+14)+(2x))/((x+2)(x))=(7(x+2)+(2x))/((x+2)(x))

(3x+5)/8-(5x-3)/10=2.5 8.5/8-(2∙2∙2∙5)/2.5=5.4 ((5)(3x+5)-(5x-3)(-4))/(2^3.5) (15x+25+20x-12)/(2^3.5)= (3x+13)/40

a/(a^2-4)-1/(a+2)=(a-2)(a+2) (a-2)(a+2)/(a-2)(a+2) -(a-2)(a+2)/(a+2)=1-(a-2)=((1)(a)-(1)(a-2))/(a-2)(a+2) = ((a)-(a-2))/((a-2)(a+2))

6x/(x^2-7x+10)-1/(x-5)=(x-5)(x-2) (x-5)(x-2)/(x-5)(x-2) -(x-5)(x-2)/((x-5) )=1-(x-2) ((1)(6x)-(x-2)(1))/((x-5) )=((6x)-(x-2))/(x-5)=(5x-2)/(x-5)

4/(x+5)+7/(x^2-25)=((x+5)(x-5))/(x+5)+((x+5)(x-5))/((x+5)(x-5))=(x-5)+1 ((4)(x-5)+(1)(7))/((x+5)(x-5))=(4x-20+7)/((x+5)(x-5))=(4x-13)/((x+5)(x-5))

8a/(a^2-8a+12)+4/(a-2)=(a-6)(a-2) ((a-6)(a-2))/((a-6)(a-2))+((a-6)(a-2))/((a-2))=1+(a-6) ((1)(8)(a-6)(4))/((a-6)(a-2))=(8+4a-24)/((a-6)(a-2) )=(4a-16)/((a-6)(a-2) O (4(a-4))/((a-6)(a-2))

6a/(a^2-10a+24)+18/(6-a)=(a-6)(a-4) ((a-6)(a-4))/((a-6)(a-4))+((a-6)(a-4))/((a-6))=1+(a-4) ((1)(6a)+(a-4)(18))/((a-6)(a-4))=(6a+18a-72)/((a-6)(a-4) ) (24a-72)/((a-6)(a-4)) O (24(a-3))/((a-6)(a-4))

3x/(x-4)+3y/(y-x)=(x-4)(x-y) (x-4)(x-y))/((x-4))+((x-4)(x-y))/((x-y))=(x-y)+(x-4)=((x-y)(3x)+(x-4)(3y))/((x-y)(x-4))=((3x^2-3xy)+(3xy-12y))/((x-y)(x-4))=

(5-4b)/8-(2-3b)/6=2^3.3 8.3/8-(2∙2∙2∙3)/6=3-4=((3)(5-4b)-(2-3b)(-4))/(2^3.3)=((15-12b)-(-8+12b))/24

x^2/(x-6)+36/(6-x)=(x-6)=((x-6))/((x-6))+(x-6))/((x-6))=1+1 ((1)(x^2 )+(36)(1))/(x-6)=(x^2+36)/(x-6)=((x+6)(x-6))/(x-6)

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