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` \color{lightblue}{Answer}`
\(\dfrac{1}{xy-x^2}-\dfrac{1}{y^2-xy}\\ =\dfrac{1}{x\left(y-x\right)}-\dfrac{1}{y\left(y-x\right)}\\ =\dfrac{y}{xy\left(y-x\right)}-\dfrac{x}{xy\left(y-x\right)}\\ =\dfrac{y-x}{xy\left(y-x\right)}\\ =\dfrac{1}{xy}\)
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\(\dfrac{x^2-4}{3x+12}.\dfrac{x+4}{2x-4}\\ =\dfrac{x^2-4}{3\left(x+4\right)}.\dfrac{x+4}{2\left(x-2\right)}\\ =\dfrac{\left(x-2\right)\left(x+2\right)}{3\left(x+4\right)}.\dfrac{x+4}{2\left(x-2\right)}\\ =\dfrac{\left(x-2\right)\left(x+2\right)\left(x+4\right)}{3\left(x+4\right)2\left(x-2\right)}\\ =\dfrac{x+2}{3.2}\\ =\dfrac{x+2}{6}\)
+, 1/xy-x2 - 1/y2 - xy
= 1 / x ( y-x ) - 1 /y ( y-x )
= 1y / xy ( y - x ) - 1x/ xy ( y - x )
= 1y - 1x / xy ( y-x)
= y - x / xy ( y -x )
= 1/ xy
+, x2 - 4 / 3x + 12 . x+4/2x - 4
= ( x - 2 ) ( x + 2 ) / 3 ( x + 4 ) . x+4 / 2 ( x - 2 )
= ( x - 2 ) ( x+2 ) ( x + 4 ) / 3 ( x + 4 ) 2 ( x - 2)
= x + 2 / 6
\(\dfrac{1}{xy-x^2}-\dfrac{1}{y^2-xy}\)
\(=\dfrac{1}{x\left(y-x\right)}-\dfrac{1}{y\left(y-x\right)}\)
\(=\dfrac{y-x}{xy\left(y-x\right)}\)
\(=\dfrac{1}{xy}\)
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\(\dfrac{x^2-4}{3x+12}.\dfrac{x+4}{2x-4}\)
\(=\dfrac{\left(x-2\right)\left(x+2\right)}{3\left(x+4\right)}.\dfrac{x+4}{2\left(x-2\right)}\)
\(=\dfrac{x+2}{6}\)
