Câu hỏi của sally hoàng

Question

rút gọn đa thức sau $\frac{2xy}{x^2-y^2}+\frac{x-y}{2x+2y}$

Dương · Accepted Answer

$\frac{2xy}{x^2-y^2}+\frac{x-y}{2x+2y}$$=\frac{2xy}{\left(x-y\right)\left(x+y\right)}+\frac{x-y}{2\left(x+y\right)}$$=\frac{4xy}{2\left(x-y\right)\left(x+y\right)}+\frac{\left(x-y\right)\left(x-y\right)}{2\left(x+y\right)\left(x-y\right)}$$=\frac{4xy+x^2-xy-xy-y^2}{2\left(x-y\right)\left(x+y\right)}$$=\frac{2xy+x^2-y^2}{2\left(x-y\right)\left(x+y\right)}$$=\frac{\left(x-y\right)^2}{2\left(x-y\right)\left(x+y\right)}$$=\frac{x-y}{2\left(x+y\right)}=\frac{x-y}{2x+2y}$Câu trả lời: $\frac{2xy}{x^2-y^2}+\frac{x-y}{2x+2y}$$=\frac{2xy}{\left(x-y\right)\left(x+y\right)}+\frac{x-y}{2\left(x+y\right)}$$=\frac{4xy}{2\left(x-y\right)\left(x+y\right)}+\frac{\left(x-y\right)\left(x-y\right)}{2\left(x+y\right)\left(x-y\right)}$$=\frac{4xy+x^2-xy-xy-y^2}{2\left(x-y\right)\left(x+y\right)}$$=\frac{2xy+x^2-y^2}{2\left(x-y\right)\left(x+y\right)}$$=\frac{\left(x-y\right)^2}{2\left(x-y\right)\left(x+y\right)}$$=\frac{x-y}{2\left(x+y\right)}=\frac{x-y}{2x+2y}$

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