\(A=\frac{x^2}{x^2-1}-\frac{x^2}{x^2+1}\left(\frac{x}{x+1}+\frac{1}{x^2+x}\right)\)

=>\(A=\frac{x^2}{\left(x-1\right)\left(x+1\right)}-\frac{x^2}{x^2+1}\left[\frac{x}{x+1}+\frac{1}{x\left(x+1\right)}\right]\)

=>\(A=\frac{x^2}{\left(x-1\right)\left(x+1\right)}-\frac{x^2}{x^2+1}\left[\frac{x^2}{x\left(x+1\right)}+\frac{1}{x\left(x+1\right)}\right]\)

=>\(A=\frac{x^2}{\left(x-1\right)\left(x+1\right)}-\frac{x^2}{x^2+1}.\frac{x^2+1}{x\left(x+1\right)}\)

=>\(A=\frac{x^2}{\left(x-1\right)\left(x+1\right)}-\frac{x}{x+1}\)

=>\(A=\frac{x^2}{\left(x-1\right)\left(x+1\right)}-\frac{x\left(x-1\right)}{\left(x+1\right)\left(x-1\right)}\)

=>\(A=\frac{x^2-x\left(x-1\right)}{\left(x-1\right)\left(x+1\right)}\)

=>\(A=\frac{x^2-x^2+x}{\left(x-1\right)\left(x+1\right)}\)

=>\(A=\frac{x}{x^2-1}\)

\(\frac{x+3}{2x-2}-\frac{4}{x^2-1}.\frac{x+1}{2}\)
\(=\frac{x+3}{2x-2}-\left(\frac{4}{x^2-1}.\frac{x+1}{2}\right)\)

\(=\frac{x+3}{2\left(x-1\right)}-\frac{4\left(x+1\right)}{2\left(x-1\right)\left(x+1\right)}\)
\(=\frac{x+3}{2\left(x-1\right)}-\frac{4}{2\left(x-1\right)}\)
\(=\frac{x+3-4}{2\left(x-1\right)}\)
\(=\frac{x-1}{2\left(x-1\right)}\)
\(=\frac{1}{2}\)

\(=\left(\frac{x^3+8}{4x}\right):\left(\frac{x^2-2x+4}{4x}\right)=\frac{\left(x+2\right)\left(x^2-2x+4\right)}{4x}.\frac{4x}{\left(x^2-2x+\right)}=x+2\)

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

\(=\frac{x}{x+1}.\frac{\left(x+1\right)^2}{x}=x+1\)

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

\(\frac{2}{xy}:\left(\frac{1}{x}-\frac{1}{y}\right)^2-\frac{x^2+y^2}{\left(x-y\right)^2}\left(ĐK:x\ne0;y\ne0\right)\)

\(=\frac{2}{xy}:\left(\frac{y-x}{xy}\right)^2-\frac{x^2+y^2}{\left(x-y\right)^2}\)

\(=\frac{2}{xy}\cdot\frac{x^2y^2}{\left(y-x\right)^2}-\frac{x^2+y^2}{\left(x-y\right)^2}\)

\(=\frac{-2xy}{\left(x-y\right)^2}+\frac{x^2+y^2}{\left(x-y\right)^2}\)

\(=\frac{-2xy+x^2+y^2}{\left(x-y\right)^2}\)

\(=\frac{\left(x-y\right)^2}{\left(x-y\right)^2}=1\)

\(\frac{2}{xy}:\left(\frac{1}{x}-\frac{1}{y}\right)^2-\frac{x^2+y^2}{\left(x-y\right)^2}\left(dk:x\ne y\ne0\right)\)

miik ko nghĩ nó là toán lớp 7 đâu bn

quy đồng lên thôi

ĐKXĐ:\(\sqrt{x}\ge0\Leftrightarrow x\ge0\)

Rút gọn: P=\(\left(\frac{\sqrt{x}-2}{x-1}-\frac{\sqrt{x}+2}{x+2\sqrt{x}+1}\right).\frac{\left(1-x\right)^2}{2}=\left(\frac{\left(\sqrt{x}-2\right)\left(\sqrt{x}+1\right)}{\left(x-1\right)\left(\sqrt{x}+1\right)}-\frac{\left(\sqrt{x}+2\right)\left(\sqrt{x}-1\right)}{\left(x-1\right)\left(\sqrt{x}+1\right)}\right).\frac{\left(x-1\right)^2}{2}\)

\(=\frac{x+\sqrt{x}-2\sqrt{x}-2-x+\sqrt{x}-2\sqrt{x}+2}{\left(x-1\right)\left(\sqrt{x}+1\right)}.\frac{\left(x-1\right)^2}{2}=\frac{2\sqrt{x}\left(x-1\right)^2}{2\left(x-1\right)\left(\sqrt{x}+1\right)}=\sqrt{x}\left(\sqrt{x}-1\right)=x-1\)