Question

Giúp em 7 8 10 được không ạ em cảm ơn

Answer 1

10: Ta có: \(\left(\dfrac{x+1}{x}\right)^2:\left[\dfrac{x^2+1}{x^2}+\dfrac{2}{x+1}\cdot\left(\dfrac{1}{x+1}+1\right)\right]\)

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

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

\(=\dfrac{\left(x+1\right)^2}{x^2}\cdot\dfrac{x^2\left(x+1\right)^2}{x^4+2x^3+x^2+x^2+2x+1+2x^3+4x^2}\)

\(=\dfrac{\left(x+1\right)^4}{x^4+4x^3+6x^2+2x+1}\)