Thực hiện phép tính:
a) (1/x + x - 2) : (1/x^2-x +1 - 3/x-1 )
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16 tháng 1 2023
a: \(=\dfrac{x^2-2x+1}{x}:\dfrac{x-1-3x^2+3x-3}{\left(x-1\right)\left(x^2-x+1\right)}\)
\(=\dfrac{\left(x-1\right)^2}{x}\cdot\dfrac{\left(x-1\right)\left(x^2-x+1\right)}{-2x^2+4x-4}\)
\(=\dfrac{\left(x-1\right)^3\cdot\left(x^2-x+1\right)}{-2x\left(x^2-2x+2\right)}\)
b: \(=\left[\dfrac{x^2-2x+1}{x^2+x+1}+\dfrac{2x^2-4x+1}{\left(x-1\right)\left(x^2+x+1\right)}+\dfrac{1}{x-1}\right]:\dfrac{2}{x^2+1}\)
\(=\dfrac{x^3-3x^2+3x+1+2x^2-4x+1+x^2+x+1}{\left(x-1\right)\left(x^2+x+1\right)}\cdot\dfrac{x^2+1}{2}\)
\(=\dfrac{x^3+3}{\left(x-1\right)\left(x^2+x+1\right)}\cdot\dfrac{x^2+1}{2}\)
NM
2
RH
14 tháng 10 2021
a) = x^2 - 9 - (x^2 + 3x - 10)
= -3x + 1
b) = 3x + 1 - 3x + 19
= 20
14 tháng 10 2021
a: \(\left(x+3\right)\left(x-3\right)-\left(x-2\right)\left(x+5\right)\)
\(=x^2-9-x^2-3x+10\)
\(=-3x+1\)
b: \(\dfrac{27x^3+1}{9x^2-3x+1}-\left(3x-19\right)\)
\(=3x+1-3x+19\)
=20
NN
3
NT
27 tháng 8 2021
a. \(\left(2x+1\right)^2-4x\left(x-1\right)=4x^2+4x+1-4x^2+4x=8x+1\)
b. \(\left(x-2\right)\left(x+2\right)-\left(x-1\right)^2=x^2-4-x^2+2x-1=2x-5\)
28 tháng 12 2021
\(a,\left(x-2\right)\left(x+3\right)-x\left(x-5\right)=x^2-2x+3x-6-x^2+5x=6x-6\)
\(b,\dfrac{1}{x-2}+\dfrac{-2}{x+2}+\dfrac{2x-8}{x^2-4}=\dfrac{x+2}{\left(x-2\right)\left(x+2\right)}-\dfrac{2\left(x-2\right)}{\left(x+2\right)\left(x-2\right)}+\dfrac{2x-8}{\left(x+2\right)\left(x-2\right)}=\dfrac{x+2}{\left(x-2\right)\left(x+2\right)}-\dfrac{2x-4}{\left(x+2\right)\left(x-2\right)}+\dfrac{2x-8}{\left(x+2\right)\left(x-2\right)}=\dfrac{x+2-2x+4+2x-8}{\left(x+2\right)\left(x-2\right)}=\dfrac{x-2}{\left(x+2\right)\left(x-2\right)}=\dfrac{1}{x+2}\)
18 tháng 2 2021
a) \(\dfrac{x^2-2x+1-x^2-2x-1+4}{\left(x+1\right)\left(x-1\right)}=\dfrac{-4\left(x-1\right)}{\left(x+1\right)\left(x-1\right)}=\dfrac{-4}{x+1}\)
18 tháng 2 2021
\(\dfrac{xy\left(x^2+y^2\right)}{xy\left(x^3\right)}.\dfrac{1}{x^2+y^2}=\dfrac{1}{x^3}\)
NT
2
7 tháng 12 2021
a) (x-2)(x+2)-x(x-1)+8
= x2-4-x2+x+8
= (x2-x2)+(-4+8)+x
= 4+x
b) bn viết lại đề đi:v
đọc khó quá.
7 tháng 12 2021
\(a,\left(2x-5\right)\left(5-x\right)=5\left(2x-5\right)-x\left(2x-5\right)=10x-25-2x^2+5x=15x-2x^2-25\\ b,\dfrac{1}{3x-2}-\dfrac{1}{3x+2}=\dfrac{3x+2-3x+2}{\left(3x-2\right)\left(3x+2\right)}=\dfrac{4}{\left(3x-2\right)\left(3x+2\right)}\)
\(c,\dfrac{3}{x-3}-\dfrac{6x}{x^2-9}+\dfrac{x}{x+3}=\dfrac{3\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}-\dfrac{6x}{\left(x-3\right)\left(x+3\right)}+\dfrac{x\left(x-3\right)}{\left(x-3\right)\left(x+3\right)}=\dfrac{3x+9-6x+x^2-3x}{\left(x-3\right)\left(x+3\right)}=\dfrac{x^2-6x+9}{\left(x-3\right)\left(x+3\right)}=\dfrac{\left(x-3\right)^2}{\left(x-3\right)\left(x+3\right)}=\dfrac{x-3}{x+3}\)
8 tháng 12 2021
Tham khảo
a)
-7x2(3x - 4y)
= -7x2.3x + 7x2ư.4y
= -21x2 + 28x2y
b)
(x - 3)(5x - 4)
= x.5x - x.4 - 3.5x + 3.4
= 5x2 - 4x - 15x + 12
= 5x2 - 19x + 12
c)
(2x - 1)2 = 4x2 - 4x + 1
d)
(x + 3)(x - 3) = x2 - 32 = x2 - 9
\(\left(\dfrac{1}{x}+x-2\right):\left(\dfrac{1}{x^2-x}+1-\dfrac{3}{x-1}\right)\)
\(=\dfrac{x^2-2x+1}{x}:\dfrac{1+x^2-x-3x}{x\left(x-1\right)}\)
\(=\dfrac{\left(x-1\right)^2}{x}\cdot\dfrac{x\left(x-1\right)}{x^2-4x+1}=\dfrac{\left(x-1\right)^3}{x^2-4x+1}\)