a) \(\dfrac{5y}{7}=\dfrac{5y.4x}{7.4x}=\dfrac{20xy}{28x}\)
b) \(\dfrac{3x\left(x+5\right)}{2\left(x+5\right)}=\dfrac{3x}{2}\)
c) \(\dfrac{x+2}{\left(x-1\right)}=\dfrac{\left(x+2\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}=\dfrac{\left(x+2\right)\left(x+1\right)}{x^2-1}\)
d) \(\dfrac{x^2-x-2}{x+1}=\dfrac{x\left(x-2\right)+1\left(x-2\right)}{x+1}=\dfrac{\left(x-2\right)\left(x+1\right)}{x+1}=x-2=\dfrac{\left(x-2\right)\left(x-1\right)}{x-1}=\dfrac{x^2-3x+2}{x-1}\)
e) \(\dfrac{x^3+8}{x^2-2x+4}=\dfrac{\left(x+2\right)\left(x^2-2x+4\right)}{x^2-2x+4}=x+2\)
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