a) Ta có: \(x+\frac{1-2x}{9}+\frac{3x-2}{12}\)
\(=\frac{36x}{36}+\frac{4\left(1-2x\right)}{36}+\frac{3\left(3x-2\right)}{36}\)
\(=\frac{36x+4-8x+9x-6}{36}\)
\(=\frac{37x-2}{36}\)
b) Ta có: \(x+y+\frac{3x^2}{2y}\)
\(=\frac{2xy}{2y}+\frac{2y^2}{2y}+\frac{3x^2}{2y}\)
\(=\frac{3x^2+2xy+2y^2}{2y}\)
c) Ta có: \(\frac{2x^2-11xy}{2xy}+\frac{5y-x}{y}+\frac{x+2y}{x}\)
\(=\frac{2x^2-11xy}{2xy}+\frac{2x\left(5y-x\right)}{2xy}+\frac{2y\left(x+2y\right)}{2xy}\)
\(=\frac{2x^2-11xy+10xy-2x^2+2xy+4y^2}{2xy}\)
\(=\frac{xy+4y^2}{2xy}\)
\(=\frac{y\left(x+4y\right)}{2xy}\)
\(=\frac{x+4y}{2x}\)
d) Ta có: \(x^2+\frac{x^4+1}{1-x^2}+1\)
\(=\frac{x^2\left(x^2-1\right)}{x^2-1}-\frac{x^4+1}{x^2-1}+\frac{x^2-1}{x^2-1}\)
\(=\frac{x^4-x^2-x^4-1+x^2-1}{x^2-1}\)
\(=\frac{-2}{x^2-1}\)
e) Ta có: \(\frac{4}{x+2}+\frac{3}{2-x}+\frac{12}{x^2-4}\)
\(=\frac{4\left(x-2\right)}{\left(x+2\right)\left(x-2\right)}-\frac{3\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}+\frac{12}{\left(x-2\right)\left(x+2\right)}\)
\(=\frac{4x-8-3x-6+12}{\left(x-2\right)\left(x+2\right)}\)
\(=\frac{x-2}{\left(x-2\right)\left(x+2\right)}\)
\(=\frac{1}{x+2}\)
