a)
\(\left(2x-5\right)^2-4x\left(x-5\right)\\ =4x^2-20x+25-4x^2+20x\\ =4x^2-4x^2-20x+20x+25\\ =25\)
b)
\(\left(9x^4y^3-15x^3y^4\right):3x^2y^2+5xy^2\\ =3x^2y-5xy^2+5xy^2\\ =3x^2y\)
c)
\(\dfrac{x}{2x-2}-\dfrac{3}{2x+2}+\dfrac{1}{1-x^2}\\ =\dfrac{x}{2\left(x-1\right)}-\dfrac{3}{2\left(x+1\right)}-\dfrac{1}{\left(x-1\right)\left(x+1\right)}\)
\(=\dfrac{x\left(x+1\right)}{2\left(x-1\right)\left(x+1\right)}-\dfrac{3\left(x-1\right)}{2\left(x-1\right)\left(x+1\right)}-\dfrac{2}{2\left(x-1\right)\left(x+1\right)}\)
\(=\dfrac{x^2+x-3x+3-2}{2\left(x-1\right)\left(x+1\right)}\\ =\dfrac{x^2-2x+1}{2\left(x-1\right)\left(x+1\right)}\\ =\dfrac{\left(x-1\right)^2}{2\left(x-1\right)\left(x+1\right)}\\ =\dfrac{x-1}{2\left(x+1\right)}\)
a)
\(\left(2x-5\right)^2-4x\left(x-5\right)\\ =4x^2-20x+25-4x^2+20x\\ =25\)
b)
\(\left(9x^4y^3-15x^3y^4\right):3x^2y^2+5xy\\ =3x^3y^3\left(3x-5y\right):3x^2y^2\\ =xy\left(3x-5y\right)\)
c)
\(\dfrac{x}{2x-2}-\dfrac{3}{2x+2}+\dfrac{1}{1-x^2}\\ =\dfrac{x\left(x+1\right)-3\left(x-1\right)+2}{2\left(x-1\right)\left(x+1\right)}\\ =\dfrac{x^2+x-3x+3+2}{2\left(x-1\right)\left(x+1\right)}\\ =\dfrac{x^2-2x+5}{2\left(x-1\right)\left(x+1\right)}\)
