ĐKXĐ: \(\left\{{}\begin{matrix}3x\ne-y\\3x\ne y\end{matrix}\right.\)
a. \(\dfrac{x}{3x+y}+\dfrac{x}{3x-y}-\dfrac{2xy}{y^2-9x^2}\)
\(=\dfrac{x.\left(3x-y\right)}{\left(3x+y\right).\left(3x-y\right)}+\dfrac{x.\left(3x+y\right)}{\left(3x+y\right).\left(3x-y\right)}+\dfrac{2xy}{9x^2-y^2}\)
\(=\dfrac{x.\left(3x+y+3x-y\right)+2xy}{\left(3x-y\right).\left(3x+y\right)}\)
\(=\dfrac{6x^2+2xy}{\left(3x-y\right).\left(3x+y\right)}\)
\(=\dfrac{2x\left(3x+y\right)}{\left(3x+y\right).\left(3x-y\right)}\)
\(=\dfrac{2x}{3x-y}\)
ĐKXĐ: \(\left\{{}\begin{matrix}x\ne0\\x\ne-5\end{matrix}\right.\)
b. \(\dfrac{4x+5}{x^2+5x}-\dfrac{3}{x+5}\)
\(=\dfrac{4x+5}{x.\left(x+5\right)}-\dfrac{3x}{x.\left(x+5\right)}\)
\(=\dfrac{x+5}{x.\left(x+5\right)}\)
\(=\dfrac{1}{x}\)
a) Ta có: \(\dfrac{x}{3x+y}+\dfrac{x}{3x-y}-\dfrac{2xy}{y^2-9x^2}\)
\(=\dfrac{x\left(3x-y\right)}{\left(3x+y\right)\left(3x-y\right)}+\dfrac{x\left(3x+y\right)}{\left(3x+y\right)\left(3x-y\right)}+\dfrac{2xy}{\left(3x+y\right)\left(3x-y\right)}\)
\(=\dfrac{3x^2-xy+3x^2+xy+2xy}{\left(3x+y\right)\left(3x-y\right)}\)
\(=\dfrac{6x^2+2xy}{\left(3x+y\right)\left(3x-y\right)}\)
\(=\dfrac{2x\left(3x+y\right)}{\left(3x+y\right)\left(3x-y\right)}\)
\(=\dfrac{2x}{3x-y}\)
b) Ta có: \(\dfrac{4x+5}{x^2+5x}-\dfrac{3}{x+5}\)
\(=\dfrac{4x+5}{x\left(x+5\right)}-\dfrac{3x}{x\left(x+5\right)}\)
\(=\dfrac{4x+5-3x}{x\left(x+5\right)}\)
\(=\dfrac{x+5}{x\left(x+5\right)}\)
\(=\dfrac{1}{x}\)
