Question

Cho biểu thức \(A=\left(\dfrac{x+1}{x-1}-\dfrac{x-1}{x+1}\right)\div\dfrac{2x}{5x-5}\). Tìm x để A có giá trị âm

Answer 1

ĐKXĐ: \(x\notin\left\{1;-1;0\right\}\)

\(A=\left(\dfrac{x+1}{x-1}-\dfrac{x-1}{x+1}\right):\dfrac{2x}{5x-5}\)

\(=\dfrac{\left(x+1\right)^2-\left(x-1\right)^2}{\left(x-1\right)\left(x+1\right)}\cdot\dfrac{5x-5}{2x}\)

\(=\dfrac{x^2+2x+1-x^2+2x-1}{\left(x-1\right)\left(x+1\right)}\cdot\dfrac{5\left(x-1\right)}{2x}\)

\(=\dfrac{4x\cdot5}{2x\left(x+1\right)}=\dfrac{20}{2\left(x+1\right)}=\dfrac{10}{x+1}\)

Để A<0 thì \(\dfrac{10}{x+1}< 0\)

=>x+1<0

=>x<-1