Question

Cho B = [ 3x/( 1-3x ) + 2x/(3x+1) ] : 6x^2 + 10x/1-6x + 9x^2

a,Rút gọn B

b, Tính gtrị của B khi B = 1/3

c, tìm x để B > 0

Answer 1

https://i.imgur.com/xpomZlu.jpg

Answer 2

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 :

\(-\dfrac{1}{3}< x< \dfrac{1}{3}\)