\(a,\dfrac{16+x}{x^2-2x}+\dfrac{18}{2x-x^2}\)
\(=\dfrac{16+x}{x^2-2x}-\dfrac{18}{x^2-2x}\)
\(=\dfrac{16+x-18}{x^2-2x}\)
\(=\dfrac{x-2}{x\left(x-2\right)}\)
\(=\dfrac{1}{x}\)
\(b,\dfrac{2y}{2x^2-xy}+\dfrac{4x}{xy-2x^2}\)
\(=\dfrac{2y}{2x^2-xy}-\dfrac{4x}{2x^2-xy}\)
\(=\dfrac{2y-4x}{2x^2-xy}\)
\(=\dfrac{2\left(y-2x\right)}{x\left(2x-y\right)}\)
\(=\dfrac{-2\left(2x-y\right)}{x\left(2x-y\right)}\)
\(=-\dfrac{2}{x}\)
\(c,\dfrac{4-x^2}{x-3}+\dfrac{2x-2x^2}{3-x}+\dfrac{5-4x}{x-3}\)
\(=\dfrac{4-x^2}{x-3}-\dfrac{2x^2-2x}{x-3}+\dfrac{5-4x}{x-3}\)
\(=\dfrac{4-x^2-2x^2+2x+5-4x}{x-3}\)
\(=\dfrac{-3x^2-2x+9}{x-3}\)
\(a,\dfrac{16+x}{x^2-2x}+\dfrac{18}{2x-x^2}\)
\(=\dfrac{16+x}{x^2-2x}-\dfrac{18}{x^2-2x}\)
\(=\dfrac{16+x-18}{x^2-2x}\)
\(=\dfrac{x-2}{x\left(x-2\right)}\)
\(=\dfrac{1}{x}\)
\(b,\dfrac{2y}{2x^2-xy}+\dfrac{4x}{xy-2x^2}\)
\(=\dfrac{2y}{2x^2-xy}-\dfrac{4x}{2x^2-xy}\)
\(=\dfrac{2y-4x}{2x^2-xy}\)
\(=\dfrac{2\left(y-2x\right)}{x\left(2x-y\right)}\)
\(=\dfrac{-2\left(2x-y\right)}{x\left(2x-y\right)}\)
\(=-\dfrac{2}{x}\)
\(c,\dfrac{4-x^2}{x-3}+\dfrac{2x-2x^2}{3-x}+\dfrac{5-4x}{x-3}\)
\(=\dfrac{4-x^2}{x-3}-\dfrac{2x^2-2x}{x-3}+\dfrac{5-4x}{x-3}\)
\(=\dfrac{4-x^2-2x^2+2x+5-4x}{x-3}\)
\(=\dfrac{-3x^2-2x+9}{x-3}\)
a,16+xx2−2x+182x−x2a,16+xx2−2x+182x−x2
=16+xx2−2x−18x2−2x=16+xx2−2x−18x2−2x
=16+x−18x2−2x=16+x−18x2−2x
=x−2x(x−2)=x−2x(x−2)
=1x=1x
b,2y2x2−xy+4xxy−2x2b,2y2x2−xy+4xxy−2x2
=2y2x2−xy−4x2x2−xy=2y2x2−xy−4x2x2−xy
=2y−4x2x2−xy=2y−4x2x2−xy
=2(y−2x)x(2x−y)=2(y−2x)x(2x−y)
=−2(2x−y)x(2x−y)=−2(2x−y)x(2x−y)
=−2x=−2x
c,4−x2x−3+2x−2x23−x+5−4xx−3c,4−x2x−3+2x−2x23−x+5−4xx−3
=4−x2x−3−2x2−2xx−3+5−4xx−3=4−x2x−3−2x2−2xx−3+5−4xx−3
=4−x2−2x2+2x+5−4xx−3=4−x2−2x2+2x+5−4xx−3
=−3x2−2x+9x−3