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2 tháng 12 2023
Bài 3:
3: \(6x\left(x-y\right)-9y^2+9xy\)
\(=6x\left(x-y\right)+9xy-9y^2\)
\(=6x\left(x-y\right)+9y\left(x-y\right)\)
\(=\left(x-y\right)\left(6x+9y\right)\)
\(=3\left(2x+3y\right)\left(x-y\right)\)
Bài 4:
2 tháng 12 2023
Bài 4:
1: \(\left(x-1\right)\left(x^2+x+1\right)-x^3-6x=11\)
=>\(x^3-1-x^3-6x=11\)
=>-6x-1=11
=>-6x=11+1=12
=>\(x=\dfrac{12}{-6}=-2\)
2: \(16x^2-\left(3x-4\right)^2=0\)
=>\(\left(4x\right)^2-\left(3x-4\right)^2=0\)
=>\(\left(4x-3x+4\right)\left(4x+3x-4\right)=0\)
=>(x+4)(7x-4)=0
=>\(\left[{}\begin{matrix}x+4=0\\7x-4=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-4\\x=\dfrac{4}{7}\end{matrix}\right.\)
3: \(x^3-x^2-3x+3=0\)
=>\(\left(x^3-x^2\right)-\left(3x-3\right)=0\)
=>\(x^2\left(x-1\right)-3\left(x-1\right)=0\)
=>\(\left(x-1\right)\left(x^2-3\right)=0\)
=>\(\left[{}\begin{matrix}x-1=0\\x^2-3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\x^2=3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\x=\sqrt{3}\\x=-\sqrt{3}\end{matrix}\right.\)
4: \(\dfrac{x-1}{x+2}=\dfrac{x+2}{x+1}\)(ĐKXĐ: \(x\notin\left\{-2;-1\right\}\))
=>\(\left(x+2\right)^2=\left(x-1\right)\left(x+1\right)\)
=>\(x^2+4x+4=x^2-1\)
=>4x+4=-1
=>4x=-5
=>\(x=-\dfrac{5}{4}\left(nhận\right)\)
5: ĐKXĐ: \(x\notin\left\{0;-1\right\}\)
\(\dfrac{1}{x}+\dfrac{2}{x+1}=0\)
=>\(\dfrac{x+1+2x}{x\left(x+1\right)}=0\)
=>3x+1=0
=>3x=-1
=>\(x=-\dfrac{1}{3}\left(nhận\right)\)
6: ĐKXĐ: \(x\notin\left\{0;3\right\}\)
\(\dfrac{9-x^2}{x}:\left(x-3\right)=1\)
=>\(\dfrac{-\left(x^2-9\right)}{x\left(x-3\right)}=1\)
=>\(\dfrac{-\left(x-3\right)\left(x+3\right)}{x\left(x-3\right)}=1\)
=>\(\dfrac{-x-3}{x}=1\)
=>-x-3=x
=>-2x=3
=>\(x=-\dfrac{3}{2}\left(nhận\right)\)
AH
Akai Haruma
Giáo viên
19 tháng 12 2022
Bạn cần viết lại đề bằng công thức toán (biểu tượng $\sum$ góc trái khung soạn thảo). Viết như thế này nhìn khó đọc quá.
26 tháng 2 2021
Ta có: \(\left(\dfrac{x+2}{3x}+\dfrac{2}{x+1}-3\right):\dfrac{2-4x}{x+1}\cdot\dfrac{3x}{x^2-3x-1}\)
\(=\left(\dfrac{\left(x+2\right)\left(x+1\right)}{3x\left(x+1\right)}+\dfrac{6x}{3x\left(x+1\right)}-\dfrac{9x\left(x+1\right)}{3x\left(x+1\right)}\right):\dfrac{2-4x}{x+1}\cdot\dfrac{3x}{x^2-3x-1}\)
\(=\dfrac{x^2+3x+2+6x-9x^2-9x}{3x\left(x+1\right)}\cdot\dfrac{x+1}{2-4x}\cdot\dfrac{3x}{x^2-3x-1}\)
\(=\dfrac{-8x^2+2}{3x\left(x+1\right)}\cdot\dfrac{x+1}{2-4x}\cdot\dfrac{3x}{x^2-3x-1}\)
\(=\dfrac{-2\left(4x^2-1\right)}{3x\cdot2\cdot\left(1-2x\right)}\cdot\dfrac{3x}{x^2-3x-1}\)
\(=\dfrac{2\left(1-2x\right)\left(2x+3\right)}{6x\left(1-2x\right)}\cdot\dfrac{3x}{x^2-3x-1}\)
\(=\dfrac{2x+3}{x^2-3x-1}\)
2 tháng 8 2023
\(\dfrac{6}{x^2+4x}+\dfrac{3}{2x+8}\\ =\dfrac{6}{x\left(x+4\right)}+\dfrac{3}{2\left(x+4\right)}\\ =\dfrac{6.2}{2x\left(x+4\right)}+\dfrac{3x}{2x\left(x+4\right)}\\ =\dfrac{12+3x}{2x\left(x+4\right)}\\ =\dfrac{3\left(4+x\right)}{2x\left(x+4\right)}\\ =\dfrac{3}{2x}\)
________
\(\dfrac{x+1}{x-2}+\dfrac{x-2}{x+2}+\dfrac{x-14}{x^2-4}\\ \left(\text{đ}k\text{x}\text{đ}:x\ne\pm2\right)\\ =\dfrac{\left(x+1\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}+\dfrac{\left(x-2\right)^2}{\left(x+2\right)\left(x-2\right)}+\dfrac{x-14}{\left(x-2\right)\left(x+2\right)}\\ =\dfrac{x^2+2x+x+2+x^2-4x+4+x-14}{\left(x-2\right)\left(x+2\right)}\\ =\dfrac{2x^2-8}{\left(x-2\right)\left(x+2\right)}\\ =\dfrac{2\left(x^2-4\right)}{x^2-4}\\ =2\)
2 tháng 8 2023
a: \(=\dfrac{6}{x\left(x+4\right)}+\dfrac{3}{2\left(x+4\right)}\)
\(=\dfrac{12+3x}{2x\left(x+4\right)}=\dfrac{3\left(x+4\right)}{2x\left(x+4\right)}=\dfrac{3}{2x}\)
b: \(=\dfrac{\left(x+1\right)\left(x+2\right)+\left(x-2\right)^2+x-14}{x^2-4}\)
\(=\dfrac{x^2+3x+2+x^2-4x+4+x-14}{x^2-4}=\dfrac{2x^2-8}{x^2-4}=2\)
23 tháng 10 2023
a: \(\dfrac{6}{x^2+4x}+\dfrac{3}{2x+8}\)
\(=\dfrac{6}{x\left(x+4\right)}+\dfrac{3}{2\left(x+4\right)}\)
\(=\dfrac{12+3x}{2x\left(x+4\right)}=\dfrac{3\left(x+4\right)}{2x\left(x+4\right)}=\dfrac{3}{2x}\)
b: \(\dfrac{x+1}{2x-2}+\dfrac{x-1}{2x+2}+\dfrac{x^2}{1-x^2}\)
\(=\dfrac{x+1}{2\left(x-1\right)}+\dfrac{x-1}{2\left(x+1\right)}-\dfrac{x^2}{\left(x-1\right)\left(x+1\right)}\)
\(=\dfrac{\left(x+1\right)^2+\left(x-1\right)^2-2x^2}{2\left(x-1\right)\left(x+1\right)}\)
\(=\dfrac{x^2+2x+1+x^2-2x+1-2x^2}{2\left(x-1\right)\left(x+1\right)}=\dfrac{2}{2\left(x-1\right)\left(x+1\right)}=\dfrac{1}{x^2-1}\)
c: \(\dfrac{1}{x^2+xy}+\dfrac{2}{y^2-x^2}+\dfrac{1}{xy-x^2}\)
\(=\dfrac{1}{x\left(x+y\right)}-\dfrac{2}{\left(x-y\right)\left(x+y\right)}-\dfrac{1}{x\left(x-y\right)}\)
\(=\dfrac{x-y-2x-x-y}{x\left(x-y\right)\left(x+y\right)}=\dfrac{-2x-2y}{x\left(x-y\right)\left(x+y\right)}\)
\(=-\dfrac{2}{x\left(x-y\right)}\)
Trả lời:
a, ( x + 1 )2 + ( x - 2 ) ( x + 3 ) - 4x
= x2 + 2x + 1 + x2 + 3x - 2x - 6 - 4x
= 2x2 - x - 5
b, ( x - 2 )2 + ( x + 1 )2 + 2 ( x - 2 ) ( - 1 - x )
= x2 - 4x - 4 + x2 + 2x + 1 + ( 2x - 4 ) ( - 1 - x )
= 2x2 - 2x - 3 - 2x - 2x2 + 4x + 4x
= 4x - 3
a) \(\left(x+1\right)^2+\left(x-2\right)\left(x+3\right)-4x\)
\(=\left(x^2+2x+1\right)+\left(x^2+x-6\right)-4x\)
\(=x^2+2x+1+x^2+x-6-4x\)
\(=2x^2-x-5\)
b) \(\left(x-2\right)^2+\left(x+1\right)^2+2\left(x-2\right)\left(-1-x\right)\)
\(=\left(x^2-4x+4\right)+\left(x^2+2x+1\right)+\left(2x-4\right)\left(-1-x\right)\)
\(=x^2-4x+4+x^2+2x+1+\left(-2x-2x^2+4+4x\right)\)
\(=x^2-4x+4+x^2+2x+1-2x-2x^2+4+4x\)
\(=9\)