Which of the following is equal to the rational expression when x ≠ 5 or -1? ((x-7)(x+1))/((x+1)(x-5)) a. (x+1)/(x-7) b. (x+1)/(x-5) c. (x-7)/(x+1) d. (x-7)/(x-5)

Question

Which of the following is equal to the rational expression when x ≠ 5 or -1?


`((x-7)(x+1))/((x+1)(x-5))`

a.
`(x+1)/(x-7)`
b.
`(x+1)/(x-5)`
c.
`(x-7)/(x+1)`
d.
`(x-7)/(x-5)`

Answer 1

When x ≠ 5 and x ≠ -1, the expression can be simplified by cancelling the common factor in the numerator and denominator, namely (x+1) to leave us with (x-7) / (x-5), for which there is only one valid choice out of the four.

Answer 2

`((x-7))/((x-5))`

option D is correct

Explanation:

`((x-7)(x+1))/((x+1)(x-5))`

In an rational expression , if we have same factors at the top and bottom then we cancel it out

In our given rational expression we have x+1 at the top and bottom

so we cancel out x+1

After cancelling out x+1, we are left with

`((x-7))/((x-5))`

option D is correct