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Which of the following is equal to the rational expression when x ≠ 5 or -1?
 [tex] \frac{(x-7)(x+1)}{(x+1)(x-5)} [/tex]

a. [tex] \frac{x+1}{x-7} [/tex]
b. [tex] \frac{x+1}{x-5} [/tex]
c. [tex] \frac{x-7}{x+1} [/tex]
d. [tex] \frac{x-7}{x-5} [/tex]

Respuesta :

mathmate
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:

[tex]\frac{(x-7)}{(x-5)}[/tex]

option D is correct

Step-by-step explanation:

[tex]\frac{(x-7)(x+1)}{(x+1)(x-5)}[/tex]

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

[tex]\frac{(x-7)}{(x-5)}[/tex]

option D is correct



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