\(Ghpt:\left\{{}\begin{matrix}x^2+y^2+\dfrac{8xy}{x+y}=16\\\sqrt{x+y}=x^2-y\end{matrix}\right.\)

\(Ghpt:\left\{{}\begin{matrix}x-\dfrac{1}{x^3}=y-\dfrac{1}{y^3}\\\left(x-4y\right)\left(2x-y+4\right)=-36\end{matrix}\right.\)

\(Ghpt:\left\{{}\begin{matrix}\sqrt{3x}\left(1+\dfrac{1}{x+y}\right)=2\\\sqrt{7y}\left(1-\dfrac{1}{x+y}\right)=4\sqrt{2}\end{matrix}\right.\)

\(Ghpt:\left\{{}\begin{matrix}x^3-y^3=35\\2x^2+3y^2=4x-3y\end{matrix}\right.\)

\(\dfrac{1}{x+2}+\dfrac{5}{2x^2+3x-2}\\ =\dfrac{2x+1}{\left(2x+1\right)\left(x+2\right)}+\dfrac{5}{2x^2+4x-x-2}\\ =\dfrac{2x-1}{\left(2x-1\right)\left(x+2\right)}+\dfrac{5}{2x\left(x+2\right)-\left(x+2\right)}\\ =\dfrac{2x-1}{\left(2x-1\right)\left(x+2\right)}+\dfrac{5}{\left(2x-1\right)\left(x+2\right)}\\ =\dfrac{2x-1+5}{\left(2x-1\right)\left(x+2\right)}\\ =\dfrac{2x+4}{\left(2x-1\right)\left(x+2\right)}\\ =\dfrac{2\left(x+2\right)}{\left(2x-1\right)\left(x+2\right)}\\ =\dfrac{2}{2x-1}\)

`(2x-3)^2 -4(x-3)(x+3)+2(6x+983)`

`=(4x^2 -12x+9)-4(x^2 -9)+12x+1966`

`=4x^2 -12x+9-4x^2 +36+12x+1966`

`=2011`

`-x^2 +7x-6`

`=-x^2 +6x+x-6`

`=x(6-x)-(6-x)`

`=(x-1)(6-x)`

`70xx x -70xx28 =490`

`70xx (x-28)=490`

`x-28=490:70`

`x-28=7`

`x=7+28`

`x=35`

\(\dfrac{-3}{14}+\dfrac{8}{25}\\= \dfrac{-75}{350}+\dfrac{112}{350}\\ =\dfrac{-75+112}{350}\\ =\dfrac{37}{350}\)