giải phương trình
a) 7/x+2+2/x+3=1/x ²+5x+6
b)4/x-2+x/x+1=x ²-2/x ²-x-2
c)x/x+2-x ²+1/x ²-2x-8=3/x-4
d) x/2x+1-2/x-3=x ²+5/2x ²-5x-3
giải phương trình
a) 7/x+2+2/x+3=1/x ²+5x+6
b)4/x-2+x/x+1=x ²-2/x ²-x-2
c)x/x+2-x ²+1/x ²-2x-8=3/x-4
d) x/2x+1-2/x-3=x ²+5/2x ²-5x-3
`a)`
`7/(x+2)+2/(x+3)=1/(x²+5x+6)` `(`ĐKXĐ `x\ne -2` ;`x \ne -3“)`
`⇔ (7(x+3)+2(x+2))/((x+2).(x+3))=1/((x+2)(x+3))`
`⇒ 7x + 21+2x+4=1`
`⇔ 9x +25 =1`
`⇔ 9x=-24`
`⇔ x= (-8)/3` `(TMĐK)`
`b)`
`4/(x-2)+x/(x+1)=(x²-2)/(x²-x-2)` `(`ĐKXĐ `x\ne -1` ;`x \ne 2“)`
`⇔(4(x+1)+x(x-2))/((x-2)(x+1))=(x²-2)/((x+1)(x-2))`
`⇒ 4x +4 + x² -2x=x²-2`
`⇔ 2x + x² -x² =-2-4`
`⇔ 2x = -6`
`⇔ x=-3` `(TMĐK)`
`c)`
`x/(x+2)-(x²+1)/(x²-2x-8)=3/(x-4)` `(`ĐKXĐ `x\ne -2` ;`x \ne 4“)`
`⇔x/(x+2)-(x²+1)/(x²-2x-8)-3/(x-4)=0`
`⇔ (x(x-4)-(x²+1)-3(x+2))/((x+2).(x-4))=0`
`⇒ x² -4x-x²-1 -3x -6=0`
`⇔ -7x -7=0`
`⇔ -7x=7`
`⇔ x=-1` `(TMĐK)`
`d)`
`x/(2x+1)-2/(x-3)=(x²+5)/(2x ²-5x-3)` `(`ĐKXĐ `x\ne -0,5` ;`x \ne 3“)`
`⇔ (x(x-3)-2(2x+1))/((2x+1).(x-3))=(x²+5)/((2x+1).(x-3)`
`⇒ x² -3x-4x -2=x²+5`
`⇔ x² -x² -7x=5 +2`
`⇔ -7x=7`
`⇔ x=-1` `(TMĐK)`
Đáp án:
`↓↓`
Giải thích các bước giải:
A,`7/(x+2)+2/(x+3)=1/(x²+5x+6)` (ĐKXĐ `x≠-2 ;x≠-3)`
`⇔ (7(x+3)+2(x+2))/((x+2).(x+3))=1/((x+2)(x+3))`
`⇒7x+21+2x+4=1`
`⇔ 9x +25 =1`
`⇔9x=-24`
`⇔x=-83` `(TMĐK)`
B, `4/(x-2)+x/(x+1)=(x²-2)/(x²-x-2)` `(ĐKXĐ` `x≠-1 ;x≠2)`
`⇔(4(x+1)+x(x-2))/((x-2)(x+1))=(x²-2)/((x+1)(x-2))`
`⇒4x+4+x²-2x=x²-2`
`⇔2x+x²-x²=-2-4`
`⇔2x=-6`
`⇔x=-3` `(TMĐK)`
C, `x/(x+2)-(x²+1)/(x²-2x-8)=3/(x-4)` (ĐKXĐ`x≠-2 ;x≠4)`
`⇔x/(x+2)-(x²+1)/(x²-2x-8)-3/(x-4)=0`
`⇔ (x(x-4)-(x²+1)-3(x+2))/((x+2).(x-4))=0`
`⇒x²-4x-x²-1-3x-6=0`
`⇔-7x-7=0`
`⇔-7x=7`
`⇔x=-1“(TMĐK)`
D,`x/(2x+1)-2/(x-3)=(x²+5)/(2x ²-5x-3)` `(ĐKXĐ` `x≠-0,5 ;x≠3)`
⇔ `(x(x-3)-2(2x+1))/((2x+1).(x-3))=(x²+5)/((2x+1).(x-3)`
`⇒x²-3x-4x-2=x²+5`
`⇔x²-x²-7x=5+2`
`⇔-7x=7`
`⇔x=-1` `(TMĐK)`
Học tốt!!!