Toán Lớp 8: Thực hiện phép cộng:
$a)$$\frac{2x+1}{2x-1}+$ $\frac{2}{2x^{2}+x}+$ $\frac{4x^{2}+6x-2}{x-4x^{3}}$
$b)$$\frac{x}{x+1}+$ $\frac{1}{1-x^{2}}+$ $\frac{x^{5}+x+1}{x^{4}+x^{3}-x-1}$
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Toán Lớp 8: Thực hiện phép cộng:
$a)$$\frac{2x+1}{2x-1}+$ $\frac{2}{2x^{2}+x}+$ $\frac{4x^{2}+6x-2}{x-4x^{3}}$
$b)$$\frac{x}{x+1}+$ $\frac{1}{1-x^{2}}+$ $\frac{x^{5}+x+1}{x^{4}+x^{3}-x-1}$
Comments ( 2 )
Mong cho lời giải hay nhất ❤️⭐️
$a,$ $ĐKXĐ:x\neq 0;\dfrac{1}{2}; -\dfrac{1}{2}$
$\dfrac{2x+1}{2x-1}+\dfrac{2}{2x^2+x}+\dfrac{4x^2+6x-2}{x-4x^3}$
$=\dfrac{2x+1}{2x-1}+\dfrac{2}{x(2x+1)}+\dfrac{4x^2+6x-2}{-x(4x^2-1)}$
$=\dfrac{2x+1}{2x-1}+\dfrac{2}{x(2x+1)}-\dfrac{4x^2+6x-2}{x(2x-1)(2x+1)}$
$=\dfrac{x(2x+1)^2}{x(2x-1)(2x+1)}+\dfrac{2(2x-1)}{x(2x+1)(2x-1)}-\dfrac{4x^2+6x-2}{x(2x-1)(2x+1)}$
$=\dfrac{x(4x^2+4x+1)}{x(2x-1)(2x+1)}+\dfrac{4x-2}{x(2x+1)(2x-1)}-\dfrac{4x^2+6x-2}{x(2x-1)(2x+1)}$
$=\dfrac{4x^3+4x^2+x}{x(2x-1)(2x+1)}+\dfrac{4x-2}{x(2x+1)(2x-1)}-\dfrac{4x^2+6x-2}{x(2x-1)(2x+1)}$
$=\dfrac{4x^3+4x^2+x+4x-2-4x^2-6x+2}{x(2x-1)(2x+1)}$
$=\dfrac{4x^3-x}{x(2x-1)(2x+1)}$
$=\dfrac{x(4x^2-1)}{x(2x-1)(2x+1)}$
$=\dfrac{x(2x-1)(2x+1)}{x(2x-1)(2x+1)}$
$=1$
$b,$ $ĐKXĐ:x\neq 0;-1;1$
$\dfrac{x}{x+1}+\dfrac{1}{1-x^2}+\dfrac{x^5+x+1}{x^4+x^3-x-1}$
$=\dfrac{x}{x+1}-\dfrac{1}{x^2-1}+\dfrac{x^5+x+1}{x^3(x+1)-(x+1)}$
$=\dfrac{x}{x+1}-\dfrac{1}{x^2-1}+\dfrac{x^5-x^2+x^2+x+1}{(x+1)(x^3-1)}$
$=\dfrac{x}{x+1}-\dfrac{1}{x^2-1}+\dfrac{x^2(x^3-1)+x^2+x+1}{(x+1)(x-1)(x^2+x+1)}$
$=\dfrac{x}{x+1}-\dfrac{1}{x^2-1}+\dfrac{x^2(x-1)(x^2+x+1)+x^2+x+1}{(x+1)(x-1)(x^2+x+1)}$
$=\dfrac{x}{x+1}-\dfrac{1}{x^2-1}+\dfrac{(x^2+x+1)(x^3-x^2+1)}{(x+1)(x-1)(x^2+x+1)}$
$=\dfrac{x}{x+1}-\dfrac{1}{(x-1)(x+1)}+\dfrac{x^3-x^2+1}{(x+1)(x-1)}$
$=\dfrac{x^2-x}{(x+1)(x-1)}-\dfrac{1}{(x-1)(x+1)}+\dfrac{x^3-x^2+1}{(x+1)(x-1)}$
$=\dfrac{x^2-x-1+x^3+x^2+1}{(x+1)(x-1)}$
$=\dfrac{x^3+2x^2-x}{(x+1)(x-1)}$ .