The rational expression we have is:
[tex]\frac{(x-5)(x+2)}{x+1}[/tex]
For a rational expression to be equal to 0, the numerator of the expression has to be equal to 0.
The numerator is: (x-5)(x+2)
That has to be equal to 0:
[tex](x-5)(x+2)=0[/tex]
Here, we apply the zero product property, which tells us that if a product is equal to 0, one of the two elements, or the two elements, are equal to 0:
[tex]\begin{gathered} x-5=0 \\ x+2=0 \end{gathered}[/tex]
We solve the two equations, and get the two values that will make the rational equation equal to 0:
[tex]\begin{gathered} x=5 \\ x=-2 \end{gathered}[/tex]
Answer:
E. 5
F. -2
