Question

4, thực hiện các phép tính sau :

a,\(\dfrac{\left(x+y\right)2}{x2+xy}\)+\(\dfrac{\left(x-y\right)2}{x2-xy}\)

b\(\dfrac{x2-4x}{xy-4-3y+12}\)+\(\dfrac{x-2}{y-4}\)

c,\(\dfrac{y2}{xy-5x+y-5}\)+\(\dfrac{2}{x+1}\)

Answer 1

\(\dfrac{\left(x+y\right)2}{x2+xy}+\dfrac{\left(x-y\right)2}{x2-xy}=-\left(\dfrac{\left(x-y\right)2}{x2-xy}\right)+\dfrac{\left(x-y\right)2}{x2-xy}=0\)

Answer 2

b: \(\dfrac{x^2-4x}{xy-4x-3y+12}+\dfrac{x-2}{y-4}\)

\(=\dfrac{x\left(x-4\right)}{\left(y-4\right)\left(x-3\right)}+\dfrac{x-2}{y-4}\)

\(=\dfrac{x^2-4x+x^2-5x+6}{\left(y-4\right)\left(x-3\right)}=\dfrac{2x^2-9x+6}{\left(y-4\right)\left(x-3\right)}\)

c: \(=\dfrac{y^2}{\left(y-5\right)\left(x+1\right)}+\dfrac{2}{x+1}\)

\(=\dfrac{y^2+2y-10}{\left(y-5\right)\left(x+1\right)}\)