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222-9+11+12:2*14+14 = ? ( )

## Toán Lớp 8: CMR : [2/(3x)-2/(x+1) .((x+1)/(3x)-x-1)]:(x-1)/x=(-2x)/(1-x)

Toán Lớp 8: CMR :
[2/(3x)-2/(x+1) .((x+1)/(3x)-x-1)]:(x-1)/x=(-2x)/(1-x)

1. Giải đáp + Lời giải và giải thích chi tiết:
Có:
VT= [ 2/(3x) – 2/(x+1) . ((x+1)/(3x) – x- 1 ) ] : (x-1)/x
VT= [ 2/(3x) – 2/(x+1) . ((x+1)/(3x) – (3x²)/(3x) – (3x)/(3x))]:(x-1)/x
VT= [ 2/(3x) – 2/(x+1). ((x+1-3x²-3x)/(3x) ) ] : (x-1)/x
VT= [ 2/(3x) – 2/(x+1) . (-3x²-2x+1)/(3x) ] : (x-1)/x
VT= [ 2/(3x) – 2/(x+1) . (-3x²-3x+x+1)/(3x)] : (x-1)/x
VT= [ 2/(3x) – 2/(x+1) . (-3x(x+1)+(x+1))/(3x)] : (x-1)/x
VT= [2/(3x) – (2(x+1)(1-3x))/((x+1).3x) ] : (x-1)/x
VT= [ 2/(3x) – (-6x²-4x+2)/(3x(x+1)] : (x-1)/x
VT= [(2(x+1))/(3x(x+1)) – (-6x²-4x+2)/(3x(x+1))] . x/(x-1)
VT= [(2x+2+6x²+4x-2)/(3x(x+1))] . x/(x-1)
VT= (6x²+6x)/(3x(x+1)) . x/(x-1)
VT= (2x(x+1))/((x+1)(x-1))
VT= (2x)/(x-1)
VT= (-2x)/(1-x)  (đpcm)

2. Giải đáp:

Lời giải và giải thích chi tiết:
[2/[3x] -2/[x+1] .([x+1]/[3x] -x-1)]:[x-1]/x
=[2/[3x]-2/[x+1]. [x+1-3x(x+1)]/[3x]]:[x-1]/x
=[2/[3x]-2/[x+1].[-3x^2 -2x+1]/[3x]]. x/[x-1]
=[ 2/[3x] -2/[x+1].[(x+1)(1-3x)]/[3x]]. x/[x-1]
=[2/[3x]-[2(1-3x)]/[3x] ]. x/[x-1]
=[2-2+6x]/[3x] . x/[x-1]
=[6x]/[3x] . x/[x-1]
= 2. x/[x-1]
=[2x]/[x-1]
=[-2x]/[1-x]
=>VT=VP(đpcm)
(Bài tham khảo)