Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
a) Điều kiện : \(x\ne\pm\dfrac{1}{3}\)
\(B=\left[\dfrac{3x}{1-3x}+\dfrac{2x}{3x+1}\right]:\dfrac{6x^2+10x}{1-6x+9x^2}\)
\(=\left(\dfrac{3x\left(3x+1\right)}{\left(1-3x\right)\left(3x+1\right)}+\dfrac{2x\left(1-3x\right)}{\left(1-3x\right)\left(3x+1\right)}\right):\dfrac{6x^2+10x}{ \left(3x-1\right)^2}\)
\(=\dfrac{9x^2+3x+2x-6x^2}{\left(1-3x\right)\left(3x+1\right)}\cdot\dfrac{\left(1-3x\right)^2}{6x^2+10x}\)
\(=\dfrac{x\left(3x+5\right)}{\left(1-3x\right)\left(3x+1\right)}\cdot\dfrac{\left(1-3x\right)^2}{2x\left(3x+5\right)}=\dfrac{1-3x}{2\left(3x+1\right)}\)
b) Sai đề = Không làm
c) B >0
=> \(\left[{}\begin{matrix}\left\{{}\begin{matrix}1-3x>0\\2\left(3x+1\right)>0\end{matrix}\right.\\\left[{}\begin{matrix}1-3x< 0\\2\left(3x+1\right)< 0\end{matrix}\right.\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x< \dfrac{1}{3}\\x>-\dfrac{1}{3}\end{matrix}\right.\\\left\{{}\begin{matrix}x>\dfrac{1}{3}\\x< -\dfrac{1}{3}\end{matrix}\right.\end{matrix}\right.\)
TH1 => \(-\dfrac{1}{3}< x< \dfrac{1}{3}\)
TH2 :Vô lí
Vậy giá trị x thỏa mãn :
\(-\dfrac{1}{3}< x< \dfrac{1}{3}\)
a. Ta có :
\(x^4-x^3-2x-4\)
\(=x^4-2x^3+x^3-2x-4\)
\(=x^3\left(x-2\right)+\left(x^3-2x^2\right)+\left(x^2-4\right)+\left(x^2-2x\right)\)
\(=x^3\left(x-2\right)+x^2\left(x-2\right)+\left(x+2\right)\left(x-2\right)+x\left(x-2\right)\)
\(=\left(x-2\right)\left(x^3+x^2+x+2+x\right)\)
\(=\left(x-2\right)\left[\left(x^3+2x\right)+\left(x^2+2\right)\right]\)
\(=\left(x-2\right)\left[x\left(x^2+2\right)+\left(x^2+2\right)\right]\)
\(=\left(x-2\right)\left(x^2+2\right)\left(x+1\right)\)
Ta lại có :
\(2x^4-3x^3+2x^2-6x-4\) ... biến đổi tương tự ta được \(\left(x^2+2\right)\left(x-2\right)\left(2x+1\right)\)
Do đó với \(x\ne2;x\ne\frac{1}{2}\) thì \(P=\frac{\left(x^2+2\right)\left(x-2\right)\left(x+1\right)}{\left(x-2\right)\left(x^2+2\right)\left(2x+1\right)}=\frac{x+1}{2x+1}\) ( = 1/2 )
Cảm ơn Let Hate Him nha! Nhưng bạn có thể biến đổi nốt phần sau giúp mình được không?
Câu 3 :
\(a,A=\left(\frac{x+1}{x-1}-\frac{x-1}{x+1}\right):\frac{2x}{5x-5}\) ĐKXđ : \(x\ne\pm1\)
\(A=\left(\frac{\left(x+1\right)^2}{\left(x-1\right)\left(x+1\right)}-\frac{\left(x-1\right)^2}{\left(x+1\right)\left(x-1\right)}\right):\frac{2x}{5\left(x-1\right)}\)
\(A=\left(\frac{x^2+2x+1-x^2+2x-1}{\left(x-1\right)\left(x+1\right)}\right).\frac{5\left(x-1\right)}{2x}\)
\(A=\frac{4x}{\left(x-1\right)\left(x+1\right)}.\frac{5\left(x-1\right)}{2x}\)
\(A=\frac{10}{x+1}\)
\(B=\left(\frac{x}{3x-9}+\frac{2x-3}{3x-x^2}\right).\frac{3x^2-9x}{x^2-6x+9}.\)
ĐKXđ : \(x\ne0;x\ne3\)
\(B=\left(\frac{x}{3\left(x-3\right)}+\frac{2x-3}{x\left(3-x\right)}\right).\frac{3x\left(x-3\right)}{x^2-6x+9}\)
\(B=\left(\frac{x^2}{3x\left(x-3\right)}+\frac{9-6x}{3x\left(x-3\right)}\right).\frac{3x\left(x-3\right)}{x^2-6x+9}\)
\(B=\frac{x^2-6x+9}{3x\left(x-3\right)}.\frac{3x\left(x-3\right)}{x^2-6x+9}=1\)
a, (4x-3)(3x+2)-(6x+1)(2x-5)+1
=12x2-8x-9x+6-12x2+30x-2x+5+1
=11x+12
b, (3x+4)2+(4x-1)2+(2+5x)(2-5x)
=9x2+24x+16+16x2-8x+1+4-25x2
=16x+21
c, (2x+1)(4x22x+1)+(2-3x)(4+6x+9x2)-9
=8x3+1+8-27x3-9
=-19x3
\(\begin{array}{l} C = \dfrac{x}{{2x - 2}} + \dfrac{{{x^2} + 1}}{{2 - 2{x^2}}}\\ C = \dfrac{x}{{2\left( {x - 1} \right)}} - \dfrac{{{x^2} + 1}}{{2\left( {{x^2} - 1} \right)}}\\ C = \dfrac{{x\left( {x + 1} \right)}}{{2\left( {x - 1} \right)}} - \dfrac{{{x^2} + 1}}{{2\left( {x - 1} \right)\left( {x + 1} \right)}}\\ C = \dfrac{{{x^2} + x - {x^2} - 1}}{{2\left( {x - 1} \right)\left( {x + 1} \right)}}\\ C = \dfrac{{x - 1}}{{2\left( {x - 1} \right)\left( {x + 1} \right)}}\\ C = \dfrac{1}{{2x + 2}} \end{array}\)
Để $C>0$ thì \(\dfrac{1}{2x+2}>0 \Rightarrow 2x+2>0 \Rightarrow 2x>-2 \Rightarrow x>-1\)