Question

For which value(s) of x will the rational expression below equal zero? Che all that apply. (x - 5)(x+2) x + 1 A.-5 B. 2 c. 1 1 D. -1 E. 5 F. -2

Answer 1

The rational expression we have is:

`((x-5)(x+2))/(x+1)`

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:

`(x-5)(x+2)=0`

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:

`\begin{gathered} x-5=0 \\ x+2=0 \end{gathered}`

We solve the two equations, and get the two values that will make the rational equation equal to 0:

`\begin{gathered} x=5 \\ x=-2 \end{gathered}`

Answer:

E. 5

F. -2