Toán Lớp 8: Rút gọn biểu thứ : A= (3/2x – 3x-3/1-2x + 2x^2+1/4x^2 -2x ) . x/2x+1

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1. Giải đáp + Lời giải và giải thích chi tiết:

   ĐK: {(x\ne 0),(x\ne 1/2),(x\ne -1/2):}

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

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

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

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

   = (8x^2-2)/(2x(2x-1)) . x/(2x+1)

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

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

   = 1

2. Gửi bạn:

   $ĐKXĐ:x\neq 0, ±\dfrac{1}{2}$

   $A=(\dfrac{3}{2x}-\dfrac{3x-3}{1-2x}+\dfrac{2x^2+1}{4x^2-2x}).\dfrac{x}{2x+1}$ 

   $A=(\dfrac{3}{2x}+\dfrac{3x-3}{2x-1}+\dfrac{2x^2+1}{4x^2-2x}).\dfrac{x}{2x+1}$ 

   $A=(\dfrac{3}{2x}+\dfrac{3x-3}{2x-1}+\dfrac{2x^2+1}{2x(2x-1)}).\dfrac{x}{2x+1}$ 

   $A=(\dfrac{3(2x-1)}{2x(2x-1)}+\dfrac{2x(3x-3)}{2x(2x-1)}+\dfrac{2x^2+1}{2x(2x-1)}).\dfrac{x}{2x+1}$ 

   $A=(\dfrac{6x-3}{2x(2x-1)}+\dfrac{6x^2-6x}{2x(2x-1)}+\dfrac{2x^2+1}{2x(2x-1)}).\dfrac{x}{2x+1}$ 

   $A=(\dfrac{6x-3+6x^2-6x+2x^2+1}{2x(2x-1)}).\dfrac{x}{2x+1}$ 

   $A=(\dfrac{8x^2-2}{2x(2x-1)}).\dfrac{x}{2x+1}$ 

   $A=\dfrac{2(4x^2-1)}{2x(2x-1)}.\dfrac{x}{2x+1}$ 

   $A=\dfrac{2(2x-1)(2x+1)}{2x(2x-1)}.\dfrac{x}{2x+1}$ 

   $A=\dfrac{2x+1}{x}.\dfrac{x}{2x+1}$ 

   $A=1$