Sửa đề: \(\left(x-2\right)^2-x\left(x-4\right)+5\)

Ta có: \(\left(x-2\right)^2-x\left(x-4\right)+5\)

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

=4+5

=9

`C4:`

`x/[x-2]+2/[2-x]=x/[x-2]-2/[x-2]=[x-2]/[x-2]=1`

`C5:[15x^2]/[17y^4] . [34y^5]/[15x^3]`

 `=[15x^2 . 2.17y^4 . y]/[17y^4 . 15x^2 . x]=[2y]/x`

`C5:[6x+18]/[(x+4)^2]:[3(x+3)]/[x+4]`

 `=[6(x+3)]/[(x+4)^2] . [x+4]/[3(x+3)]`

`=2/[x+4]`

a) Áp dụng công thức nhị thức Newton, ta có:

\(\begin{array}{l}{\left( {1 + x} \right)^4} = {1^4} + C_4^1{.1^3}x + C_4^2{.1^2}{x^2} + C_4^3.1{x^3} + C_4^4{x^4}\\ = 1 + 4x + 6{x^2} + 4{x^3} + {x^4}\end{array}\)

\(\begin{array}{l}{\left( {1 - x} \right)^4} = {1^4} + C_4^1{.1^3}\left( { - x} \right) + C_4^2{.1^2}{\left( { - x} \right)^2} + C_4^3.1{\left( { - x} \right)^3} + C_4^4{\left( { - x} \right)^4}\\ = 1 - 4x + 6{x^2} - 4{x^3} + {x^4}\end{array}\)

Suy ra

\(\begin{array}{l}{\left( {1 + x} \right)^4} + {\left( {1 - x} \right)^4} = 1 + 4x + 6{x^2} + 4{x^3} + {x^4} + 1 - 4x + 6{x^2} - 4{x^3} + {x^4}\\ = 2 + 12{x^2} + 2{x^4}\end{array}\)

Vậy \({\left( {1 + x} \right)^4} + {\left( {1 - x} \right)^4} = 2 + 12{x^2} + 2{x^4}\)

Ta có: \(1,{05^4} + 0,{95^4} = {\left( {1 + 0,05} \right)^4} + {\left( {1 - 0,05} \right)^4}\)

Áp dụng biểu thức vừa chứng minh \({\left( {1 + x} \right)^4} + {\left( {1 - x} \right)^4} = 2 + 12{x^2} + 2{x^4}\)

ta có: \(1,{05^4} + 0,{95^4} = {\left( {1 + 0,05} \right)^4} + {\left( {1 - 0,05} \right)^4} = 2 + 12.0,0{5^2} + 2.0,0{5^4}\\ = 2,0300125\)

a.\(A=\dfrac{x^2-4x+4}{x^3-2x^2-\left(4x-8\right)}=\dfrac{\left(x-2\right)^2}{x^2\left(x-2\right)-4\left(x-2\right)}=\dfrac{\left(x-2\right)^2}{\left(x^2-4\right)\left(x-2\right)}=\dfrac{x-2}{\left(x-2\right)\left(x+2\right)}=\dfrac{1}{x+2}\)

\(A=\dfrac{\left(x-2\right)^2}{x^2\left(x-2\right)-4\left(x-2\right)}\left(x\ne\pm2\right)\\ A=\dfrac{\left(x-2\right)^2}{\left(x-2\right)^2\left(x+2\right)}=\dfrac{1}{x+2}\\ B=\dfrac{x+2-x+\sqrt{x}-1}{\left(\sqrt{x}+1\right)\left(x-\sqrt{x}+1\right)}\cdot\dfrac{4\sqrt{x}}{3}\left(x>0\right)\\ B=\dfrac{4\sqrt{x}\left(\sqrt{x}+1\right)}{3\left(\sqrt{x}+1\right)\left(x-\sqrt{x}+1\right)}=\dfrac{4\sqrt{x}}{3\left(x-\sqrt{x}+1\right)}\)

Chọn C

D

D

ko phải đâu

phải d9o1` . cam đoan 1000%

Ta có: \(A=\left(\frac{\sqrt{x}}{\sqrt{x}-2}-\frac{\sqrt{x}}{\sqrt{x}+2}\right):\frac{x-\sqrt{x}}{\sqrt{x}-1}\)

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

\(=\frac{x+2\sqrt{x}-x+2\sqrt{x}}{x-4}\cdot\frac{1}{\sqrt{x}}=\frac{4\sqrt{x}}{\sqrt{x}\left(x-4\right)}=\frac{4}{x-4}\)

B

Chọn B

 Rút gọn : \(P=\left(\frac{1}{x-2}-\frac{1}{x+2}+1\right):\frac{1}{x^2-4}\)

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

\(P=\frac{x+2-x+2+x^2-4}{x^2-4}:\frac{1}{x^2-4}\)

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

\(P=x^2\)

........

mk chỉ biết làm rút gọn thôi nha