\(B=\left(x+1\right)^2-2\left(2x-1\right)\left(1+x\right)+4x^2-4x+1\)

\(=\left(x+1\right)^2-2\left(x+1\right)\left(2x-1\right)+\left(2x-1\right)^2\)

\(=\left(x+1-2x+1\right)^2=\left(2-x\right)^2\)

`@` `\text {Ans}`

`\downarrow`

\(B=(x+1)^2-2(2x-1)(1+x)+4x^2-4x+1\)

`= x^2 + 2x + 1 - 2(2x^2 + x - 1) + 4x^2 - 4x + 1`

`= 5x^2 - 2x + 2 - 4x^2 - 2x + 2`

`= x^2 - 4x + 4`

\(B=\left(x+1\right)^2-2\left(2x-1\right)\left(1+x\right)+4x^2-4x+1\)

\(=\left(x+1\right)^2-2\left(x+1\right)\left(2x-1\right)+\left(2x-1\right)^2\)

\(=\left(x+1-2x+1\right)^2\)

\(=\left(2-x\right)^2\)

ĐKXĐ : \(\left\{{}\begin{matrix}4x^2-1\ne0\\8x^3+1\ne0\end{matrix}\right.\Leftrightarrow x\ne\pm\dfrac{1}{2}\)

\(P=\dfrac{2x^5-x^4-2x+1}{4x^2-1}+\dfrac{8x^2-4x+2}{8x^3+1}\)

\(=\dfrac{\left(x^4-1\right)\left(2x-1\right)}{\left(2x-1\right)\left(2x+1\right)}+\dfrac{2\left(4x^2-2x+1\right)}{\left(2x+1\right)\left(4x^2-2x+1\right)}\)

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

https://sg.docworkspace.com/l/sIM-LioBEocfloAY

ĐKXĐ: \(x\ne\pm1\)

\(A=\left(\dfrac{\left(1+x\right)^2}{\left(1-x\right)\left(1+x\right)}-\dfrac{\left(1-x\right)^2}{\left(1-x\right)\left(1+x\right)}+\dfrac{4x^2}{\left(1-x\right)\left(1+x\right)}\right):\dfrac{4\left(x-1\right)\left(x+1\right)}{\left(x-1\right)^2}\)

\(=\left(\dfrac{x^2+2x+1-\left(x^2-2x+1\right)+4x^2}{\left(1-x\right)\left(1+x\right)}\right):\dfrac{4\left(x+1\right)}{x-1}\)

\(=\left(\dfrac{4x^2+4x}{\left(1-x\right)\left(1+x\right)}\right):\dfrac{4\left(x+1\right)}{x-1}\)

\(=\dfrac{4x\left(x+1\right)}{\left(1-x\right)\left(1+x\right)}.\dfrac{\left(x-1\right)}{4\left(x+1\right)}=-\dfrac{x}{x+1}\)

`P= 8x^3 -4x^2 +2x+1+x^3+x^2-x+1`

`P=9x^3 -3x^2+x+2`

\(\text{ P = (2x-1).4x^2+2x+1+(x+1)x^2-x+1}\)

\(\text{P =}\) \(\text{[(2x-1) . 4x^2 ]}\)\(\text{[(x+1) .x^2]}\)

\(\text{P = }\) \(\text{8x^3 - 4x^2 + 2x^3 + 2x^2 + 2x + 1 + x^3 - x + 1}\)

\(\text{P =}\) \(\text{(8x^3 + 2x^3 + x^3) + (-4x^2 + 2x^2) + (2x - x) + (1 + 1)}\)

\(\text{P =}\) \(\text{11x^3 - 2x^2 + x + 2}\)

Bài 1 : 

\(\left(x-2\right)^2-\left(x-3^2\right)=\left(x-2\right)^2-\left(x-9\right)\)

\(=x^2-4x+4-x+9=x^2-5x+13\)

Bài 2 : 

a, \(P=\frac{1-4x^2}{4x^2-4x+1}=\frac{\left(1-2x\right)\left(2x+1\right)}{\left(2x-1\right)^2}\)

\(=\frac{-\left(2x-1\right)\left(2x+1\right)}{\left(2x-1\right)^2}=\frac{-\left(2x+1\right)}{2x-1}=\frac{-2x-1}{2x-1}\)

b, Thay x = -4 ta được : 

\(\frac{-2.\left(-4\right)-1}{2.\left(-4\right)-1}=\frac{8-1}{-8-1}=-\frac{7}{9}\)

`@` `\text {Ans}`

`\downarrow`

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

`= [(2x - 3) - (2x + 3)]*[(2x - 3) + (2x + 3)]`

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

`= -6 * 4x`

`= -24x`

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

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

`A=-6.4x=-24x`

b: B=(x+1)^2-2(2x-1)(x+1)+4x^2-4x+1

=(x+1)^2-2(2x-1)(x+1)+(2x-1)^2

=(x+1-2x+1)^2

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

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

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

`=(6x^2-4x-6x^2+5x-1-3x+2)/(2x(2x-1))`

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

`=-1/(2x)`

`2x=1/(483)`

`=>A=-1/(1/483)=-483`

\(\dfrac{1-3x}{2x}+\dfrac{3x-2}{2x-1}+\dfrac{3x-2}{2x-4x^2}\)

⇔\(\dfrac{1-3x}{2x}+\dfrac{3x-2}{2x-1}+\dfrac{3x-2}{2x\left(1-2x\right)}\)

⇔\(\dfrac{1-3x}{2x}+\dfrac{3x-2}{2x-1}-\dfrac{(3x-2)}{2x\left(2x-1\right)}\)

ĐKXĐ: \(\left\{{}\begin{matrix}2x\ne0\\2x-1\ne0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ne0\\2x\ne1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ne0\\x\ne\dfrac{1}{2}\end{matrix}\right.\)

MTC: 2x(2x-1)

\(\dfrac{1-3x\left(2x-1\right)}{2x\left(2x-1\right)}+\dfrac{(3x-2)(2x)}{(2x-1)(2x)}-\dfrac{(3x-2)}{2x\left(2x-1\right)}\)

\(\Rightarrow1-3x\left(2x-1\right)+\left(3x-2\right)\left(2x\right)-\left(3x-2\right)\)

\(\Leftrightarrow1-6x^2+3x+6x^2-4x-3x+2\\ \Rightarrow-4x+3\)

Thay \(x=\dfrac{1}{966}\)vào biểu thức trên

ta có -4x+3= \(-4\times\dfrac{1}{966}+3=\dfrac{-4}{966}+3=\dfrac{-2}{483}+3=\dfrac{-2}{483}+\dfrac{1449}{483}=\dfrac{1447}{483}\)

KO

Để rút gọn biểu thức, ta sẽ thực hiện các phép tính và kết hợp các thành phần tương tự: P(2x-1).4x^2 + 2x + 1 + (x+1)x^2 - x + 1 = P(8x^3 - 4x^2) + 2x + 1 + x^3 + x^2 - x + 1 = P(8x^3) - P(4x^2) + x^3 + (2x-x) +(1+1) = **8Px^3 - 4Px^2**+ x^3 **+ x**+ **2** Vậy biểu thức đã được rút gọn thành: **8Px³ - 4Px²+x³+x+2**

ok bạn