Question

Rút gọn biểu thức sau :

\(A=\dfrac{x+1}{2x-2}+\dfrac{x^2+3}{2-2x^2}+\dfrac{1}{1-x}-15\)

Ace Legona ; Hồng Phúc Nguyễn ; Adonis Baldric ; Nguyễn Huy Tú . Help meeee

Answer 1

\(A=\dfrac{x+1}{2x-2}+\dfrac{x^2+3}{2-2x^2}+\dfrac{1}{1-x}-15\)

\(A=\dfrac{x+1}{2.\left(x-1\right)}+\dfrac{x^2+3}{2.\left(1-x\right).\left(1+x\right)}+\dfrac{1}{1-x}-\dfrac{15}{1}\)

\(A=\dfrac{\left(x+1\right)^2-\left(x^2+3\right)-2.\left(x+1\right)-15.2.\left(x-1\right).\left(x+1\right)}{2.\left(x-1\right).\left(x+1\right)}\)

\(A=\dfrac{x^2+2x+1-x^2-3-2x-30.\left(x^2-1\right)}{2.\left(x-1\right).\left(x+1\right)}\)

\(A=\dfrac{-4-30x^2+30}{2.\left(x-1\right).\left(x+1\right)}\)

\(A=\dfrac{26-30x^2}{2.\left(x-1\right).\left(x+1\right)}\)

\(A=\dfrac{2.\left(13-15x^2\right)}{2.\left(x-1\right).\left(x+1\right)}\)

\(A=\dfrac{13-15x^2}{\left(x-1\right).\left(x+1\right)}\)