a) \(\dfrac{25x^3y^5z}{5x^2yz}\)
\(=\dfrac{5xy^4}{1}\)
\(=5xy^4\)
b) \(\dfrac{x^2-y^2}{x-y}\)
\(=\dfrac{\left(x-y\right)\left(x+y\right)}{x-y}\)
\(=x+y\)
c) \(\dfrac{x^3+1}{x+1}\)
\(=\dfrac{\left(x+1\right)\left(x^2-x+1\right)}{x+1}\)
\(=x^2-x+1\)
d) \(\dfrac{15xy}{10y}\)
\(=\dfrac{3x}{2}\)
e) \(\dfrac{x^2+2x+1}{x^2-1}\)
\(=\dfrac{\left(x+1\right)^2}{\left(x+1\right)\left(x-1\right)}\)
\(=\dfrac{x+1}{x-1}\)
f) \(\dfrac{x+1}{x^2+x}\)
\(=\dfrac{x+1}{x\left(x+1\right)}\)
\(=\dfrac{1}{x}\)
g) \(\dfrac{x^2+6x+9}{x^2-9}\)
\(=\dfrac{\left(x+3\right)^2}{\left(x+3\right)\left(x-3\right)}\)
\(=\dfrac{x+3}{x-3}\)
h) \(\dfrac{x-4}{x^2-16}\)
\(=\dfrac{x-4}{\left(x-4\right)\left(x+4\right)}\)
\(=\dfrac{1}{x+4}\)
