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\(a,\left(3x+1\right)\left(3x-1\right)-\left(18x^3+5x^2-2x\right):2x\\ =\left(9x^2-1\right)-\left(9x^2+\dfrac{5}{2}x-1\right)\\ =9x^2-1-9x^2-\dfrac{5}{2}x+1=\dfrac{5}{2}x\)
\(b,3x\left(x-2021\right)-x+2021=0\\ \Rightarrow b,3x\left(x-2021\right)-\left(x-2021\right)=0\\ \Rightarrow\left(x-2021\right)\left(3x-1\right)=0\\ \Rightarrow\left[{}\begin{matrix}x=2021\\x=\dfrac{1}{3}\end{matrix}\right.\)
\(=\dfrac{3x+2}{\left(x-1\right)^2}-\dfrac{6}{\left(x-1\right)\left(x+1\right)}+\dfrac{2-3x}{\left(x+1\right)^2}\\ =\dfrac{\left(3x+2\right)\left(x+1\right)^2-6\left(x^2-1\right)+\left(2-3x\right)\left(x-1\right)^2}{\left(x-1\right)^2\left(x+1\right)^2}\\ =\dfrac{10x^2+10}{\left(x-1\right)^2\left(x+1\right)^2}\)
a: =9x^2-12x+4-4x^2+14x
=5x^2+2x+4
b: \(=\dfrac{2+x+1+x-1}{2\left(x-1\right)\left(x+1\right)}=\dfrac{2x+2}{2\left(x-1\right)\left(x+1\right)}=\dfrac{1}{x-1}\)
a) 3x.(x² - 2)
= 3x.x² + 3x.(-2)
= 3x³ - 6x
b) (6x³ + 2x² - 4x) : 2x
= 6x³ : 2x + 2x² : 2x - 4x : 2x
= 3x² + x - 2
c) 2x(x² - 1)
= 2x.x² - 2x.1
= 2x³ - 2x
`a)3x(2x^2-3x+4)`
`=6x^3-9x^2+12x`
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`b)(x+3)^2+(3x-2)(x+4)`
`=x^2+6x+9+3x^2+12x-2x-8`
`=4x^2+16x+1`
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`c)[2x-4]/[x-1]+[2x+2]/[x^2-1]` `ĐK: x \ne +-1`
`=[(2x-4)(x+1)+2x+2]/[(x-1)(x+1)]`
`=[2x^2+2x-4x-4+2x+2]/[(x-1)(x+1)]`
`=[2x^2-2]/[x^2-1]`
`=2`
\(=\dfrac{2x+6}{x\left(3x-1\right)}+\dfrac{x+3}{3x-1}\)
\(=\dfrac{2x+6+x^2+3x}{x\left(3x-1\right)}\)
\(=\dfrac{x^2+5x+6}{x\left(3x-1\right)}\)
=3x(x^2-2)(3x^2+x-2)
=(3x^3-6x)(3x^2+x-2)
=9x^5+3x^4-6x^3-18x^3-6x^2+12x
=9x^5+3x^4-12x^3-6x^2+12x
2x(x^2-1)=2x^3-2x
\(\frac{x}{3x+1}+\frac{2x+1}{3x+1}=\frac{x+2x+1}{3x+1}=\frac{3x+1}{3x+1}=1\)
\(\text{CHÚC BẠN HOK TOT}\)
\(\frac{x}{3x+1}+\frac{2x+1}{3x+1}=\frac{x+2x+1}{3x+1}=\frac{\left(x+2x\right)+1}{3x+1}=\frac{3x+1}{3x+1}=1\)