Toán Lớp 8: Rút gọn:
x^2+x/x^2+x+1 – (2x^3+x^2-x/x^3-1 – 2 – 1/x-1) : 2x-1/x-x^2
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Toán Lớp 8: Rút gọn:
x^2+x/x^2+x+1 – (2x^3+x^2-x/x^3-1 – 2 – 1/x-1) : 2x-1/x-x^2
Comments ( 1 )
=$\frac{x^2+x}{x^2+x+1}$ -($\frac{2x^3+x^2-x}{(x-1)(x^2+x+1)}$ -$\frac{2(x-1)(x^2+x+1)}{(x-1)(x^2+x+1)}$ – $\frac{x^2+x+1}{(x-1)(x^2+x+1)}$ ).$\frac{x-x^2}{2x-1}$
=$\frac{x^2+x}{x^2+x+1}$ -$\frac{2x^3+x^2-x-2(x^3-1)-x^2-x-1}{(x-1)(x^2+x+1)}$ .$\frac{x-x^2}{2x-1}$
=$\frac{x^2+x}{x^2+x+1}$-$\frac{2x^3+x^2-x-2x^3+2-x^2-x-1}{(x^2+x+1)(2x-1)}$
=$\frac{(x^2+x)(2x-1)}{(x^2+x+1)(2x-1)}$-$\frac{-2x+1}{(x^2+x+1)(2x-1)}$
=$\frac{(x^2+x)(2x-1)–(2x-1)}{(x^2+x+1)(2x-1)}$
=$\frac{(x^2+x)(2x-1)+(2x-1)}{(x^2+x+1)(2x-1)}$
=$\frac{(2x-1)(x^2+x+1)}{(x^2+x+1)(2x-1)}$
=1