`a)1/(3-x)-1/(x+1)=x/(x-3)-(x-1)^2/(x^2-2x-3)` `(ĐK:x<>3;x<> -1)`

`<=>-1/(x-3)-1/(x+1)=x/(x-3)-(x-1)^2/((x+1)(x-3))`

`<=>(-(x+1))/((x+1)(x-3))-(x-3)/((x+1)(x-3))=(x(x+1))/((x+1)(x-3))-(x-1)^2/((x+1)(x-3))`

`<=>-(x+1)-(x-3)=x(x+1)-(x-1)^2`

`<=>-x-1-x+3=x^2+x-(x^2-2x+1)`

`<=>-2x+2=x^2+x-x^2+2x-1`

`<=>-2x+2=3x-1`

`<=>2x+3x=1+2`

`<=>5x=3`

`<=>x=3/5` (tm) 

`(x+3)/2-(x-1)/3=(x+5)/6+1`

`<=>(3(x+3))/6-(2(x-1))/6=(x+5)/6+6/6`

`<=>3(x+3)-2(x-1)=x+5+6`

`<=>3x+9-2x+2=x+11`

`<=>x+11=x+11`

`<=>x-x=11-11`

`<=>0=0`

Điều này luôn đúng 

`=>x∈R`

`b)(x+1)/(x^2+x+1)-(x-1)/(x^2-x+1)=(2(x+2)^2)/(x^6-1)` `(ĐK:x<>1)` 

`<=>((x+1)(x-1))/((x-1)(x^2+x+1))-((x-1)(x+1))/((x+1)(x^2-x+1))=(2(x+2)^2)/(x^6-1)`

`<=>(x^2-1)/(x^3-1)-(x^2-1)/(x^3+1)=(2(x+2)^2)/(x^6-1)`

`<=>((x^2-1)(x^3+1))/(x^6-1)-((x^2-1)(x^3-1))/(x^6-1)=(2(x+2)^2)/(x^6-1)`

`<=>(x^2-1)(x^3+1)-(x^2-1)(x^3-1)=2(x+2)^2`

`<=>x^5+x^2-x^3-1-x^5+x^2+x^3-1=2(x^2+4x+4)`

`<=>2x^2-2=2x^2+8x+8`

`<=>-2=8x+8`

`<=>8x=-10`

`<=>x=-10/8=-5/4(tm)` 

Số lượng thừa số:

`(2019-2):1+1=2018` là số chẵn

`=>(1/2-1)*(1/3-1)*...*(1/2019-1)`

`=(1-1/2)(1-1/3)*...*(1-1/2019)`

`=1/2*2/3*...*2018/2019`

`=1/2019` 

`c)x/(x-3)-x/(x-5)=x/(x-4)-x/(x-6)` `(ĐK: x<>3;x<>4;x<>5;x<>6)`

`<=>(x(x-5)-x(x-3))/((x-3)(x-5))=(x(x-6)-x(x-4))/((x-4)(x-6)`

`<=>(-2x)/((x-3)(x-5))=(-2x)/((x-4)(x-6))`

`<=>(x-3)(x-5)=(x-4)(x-6)`

`<=>x^2-3x-5x+15=x^2-4x-6x+24`

`<=>x^2-8x+15=x^2-10x+24`

`<=>-8x+10x=24-15`

`<=>2x=11`

`<=>x=11/2` 

Ta có:

`7^6+7^5-7^4`

`=7^4*(7^2+7-1)`

`=7^4*(49+7-1)`

`=7^4*55=7^4*5*11` chia hết cho 11 

Ta có:

`10^9+10^8+10^7`

`=10^7*(10^2+10+1)`

`=10^7*111`

`=10^6*5*222` chia hết cho 222 

Ta có:

`3^(n-2)-2^(n-2)+3^n-2^n`

`=(3^n+3^(n-2))-(2^n+2^(n-2)`

`=3^(n-2)*(3^2+1)-2^(n-2)*(2^2+1)`

`=3^(n-2)*10-2^(n-2)*5`

`=3^(n-2)*10-10*2^(n-3)`

`=10*(3^(n-2)-2^(n-3)` chia hết cho 10

Phần đất không dùng trồng hòa bằng:

`1-1/3=2/3` (diện tích mảnh vườn)

Phần đất còn lại bằng:

`2/3-5/12=1/4` (diện tích mảnh vườn)

ĐS: ... 

`c)(x+5)/(x^2-5x)-(x+5)/(2x^2-50)=(x-5)/(2x^2+10x)` `(ĐK:x<>+-5;x<>0)`

`<=>(x+5)/(x(x-5))-(x+5)/(2(x^2-25))=(x-5)/(2x(x+5))`

`<=>(2(x+5)^2)/(2x(x-5)(x+5))-(x(x+5))/(2x(x+5)(x-5))=(x-5)^2/((2x(x+5)(x-5))`

`<=>2(x+5)^2-x(x+5)=(x-5)^2`

`<=>2(x^2+10x+25)-x^2-5x=x^2-10x+25`

`<=>2x^2+20x+50-x^2-5x=x^2-10x+25`

`<=>x^2+15x+50=x^2-10x+25`

`<=>15x+50=-10x+25`

`<=>15x+10x=25-50`

`<=>25x=-25`

`<=>x=-1(tm)`

`a)3x^2-5x+2`

`=(3x^3-3x)+(-2x+2)`

`=3x(x-1)-2(x-1)`

`=(3x-2)(x-1)`

`b)2x^2+x-6`

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

`=x(2x-3)+2(2x-3)`

`=(2x-3)(x+2)`

`c)7x^2+50x+7`

`=(7x^2+49x)+(x+7)`

`=7x(x+7)+(x+7)`

`=(x+7)(7x+1)`

`d)12x^2+7x-12`

`=(12x^2-9x^2)+(16x-12)`

`=3x(4x-3)+4(4x-3)`

`=(4x-3)(3x-4)`

`e)15x^2+7x-2`

`=(15x^2-3x)+(10x-2)`

`=3x(5x-1)+2(5x-1)`

`=(5x-1)(3x+2)`

`xy=4(x+y)`

`<=>xy-4x-4y=0`

`<=>x(y-4)-4y+16=16`

`<=>x(y-4)-4(y-4)=16`

`<=>(x-4)(y-4)=16`

Vì x,y nguyên nên ta có bảng: