Question

Answer 1

a)

  

Answer 2

b)

 

Answer 3

c)

Answer 4

d)

  

Answer 5

a) \(\dfrac{1}{xy^3}=\dfrac{1\cdot x}{xy^3\cdot x}=\dfrac{x}{x^2y^3};\dfrac{2}{x^2y}=\dfrac{2\cdot y^2}{x^2y\cdot y^2}=\dfrac{2y^2}{x^2y^3}\)

b) \(\dfrac{1}{x^2-2x}=\dfrac{1}{x\left(x-2\right)};\dfrac{2}{x}=\dfrac{2\left(x-2\right)}{x\left(x-2\right)}=\dfrac{2x-4}{x\left(x-2\right)}\)

c) \(\dfrac{x}{x^2-9}=\dfrac{x}{\left(x-3\right)\left(x+3\right)};\dfrac{x}{x-3}=\dfrac{x\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}=\dfrac{x^2+3x}{\left(x-3\right)\left(x+3\right)}\)

d) \(\dfrac{x}{x^2+x}=\dfrac{x}{x\left(x+1\right)}=\dfrac{x\left(x-1\right)}{x\left(x+1\right)\left(x-1\right)}=\dfrac{x^2-x}{x\left(x^2-1\right)}\)

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