3) \(\dfrac{y}{xy-5y^2}-\dfrac{15y-25x}{y^2-25x^2}\) MTC: \(\left(xy-5y^2\right)\left(y^2-25x^2\right)\)
\(=\dfrac{y\left(y^2-25x^2\right)}{\left(xy-5y^2\right)\left(y^2-25x^2\right)}-\dfrac{\left(xy-5y^2\right)\left(15y-25x\right)}{\left(xy-5y^2\right)\left(y^2-25x^2\right)}\)
\(=\dfrac{y\left(y^2-25x^2\right)-\left(xy-5y^2\right)\left(15y-25x\right)}{\left(xy-5y^2\right)\left(y^2-25x^2\right)}\)
\(=\dfrac{\left(y^3-25x^2y\right)-\left(15xy^2-25x^2y-75y^3+125xy^2\right)}{\left(xy-5y^2\right)\left(y^2-25x^2\right)}\)
\(=\dfrac{y^3-25x^2y-15xy^2+25x^2y+75y^3-125xy^2}{\left(xy-5y^2\right)\left(y^2-25x^2\right)}\)
\(=\dfrac{76y^3-140xy^2}{\left(xy-5y^2\right)\left(y^2-25x^2\right)}\)
4) \(\dfrac{4-2x+x^2}{2+x}-2-x\)
\(=\dfrac{4-2x+x^2}{2+x}-\dfrac{2+x}{1}\)
\(=\dfrac{4-2x+x^2}{2+x}-\dfrac{\left(2+x\right)\left(2+x\right)}{2+x}\)
\(=\dfrac{4-2x+x^2-\left(2+x\right)\left(2+x\right)}{2+x}\)
\(=\dfrac{4-2x+x^2-\left(2+x\right)^2}{2+x}\)
\(=\dfrac{4-2x+x^2-\left(4+4x+x^2\right)}{2+x}\)
\(=\dfrac{4-2x+x^2-4-4x-x^2}{2+x}\)
\(=\dfrac{-6x}{2+x}\)
