Question

a) x+1/x-1 + 1-3x/x^3+x : x-1/x^2+1

b) (x+1/x-1 + x-1/x+1) : 5x/7x-7

( viết dưới dạng phân số nha)

Answer 1

a: \(=\dfrac{x+1}{x-1}+\dfrac{1-3x}{x^3+x}:\dfrac{x-1}{x^2+1}\)

\(=\dfrac{x+1}{x-1}+\dfrac{1-3x}{x\left(x^2+1\right)}\cdot\dfrac{x^2+1}{x-1}\)

\(=\dfrac{x+1}{x-1}+\dfrac{1-3x}{x\left(x-1\right)}\)

\(=\dfrac{x^2+x+1-3x}{x\left(x-1\right)}=\dfrac{x-1}{x}\)

b: \(=\left(\dfrac{x+1}{x-1}+\dfrac{x-1}{x+1}\right)\cdot\dfrac{7\left(x-1\right)}{5x}\)

\(=\dfrac{x^2+2x+1+x^2-2x+1}{\left(x-1\right)\left(x+1\right)}\cdot\dfrac{7\left(x-1\right)}{5x}\)

\(=\dfrac{2x^2+2}{5x}\cdot7=\dfrac{14x^2+14}{5x}\)