Math Help plz!?

Question

Find the zeros of the rational Function

f(x)= 1- 2/x-5 (f of x equals one minus two over x minus five)

In the back of my math book it says the answer is 7, but I don't get how they got that answer...

Answer 1

Substitute 0 for f(x).
0 = 1 - 2/(x-5)
Add 2/(x-5) to both sides:
2/(x-5) = 1
Multiply both sides by (x-5):
2 = x-5
x = 7

Another way to solve it:
0 = 1 - 2/(x-5)
0 = (x-5)/(x-5) - (2)/(x-5)
0 = (x-5 - 2) / (x-5)
0 = (x-7)/(x-2)
The left side is zero when the numerator is zero, when x=7.

Either way, check your answer by plugging in x=7:
f(x) = 1 - 2/(x-5)
f(x) = 1 - 2/(7-5)
f(x) = 1 - 2/2
f(x) = 1 - 1
f(x) = 0

Looks good! :)

Answer 2

To "find the zeros of the rational function", simply set f(x) as 0.
Example: 0 = 1-2/(x-5). Now, what does X have to be in order for
1-2/(x-5) to equal to zero? 7.

0 = 1-2/(x-5) --> subtract 1 from each side
-1 = -2/(x-5) -->now, multiply (x-5) for each side
-1(x-5) = -2 --> -x + 5 = -2--> now, subtract 5 from each side
-x = -7 --> now, multiply by -1 to get the value of positive x
x = 7

Like others, I don't approve of simply giving answers. However, I do like to give the principle behind WHY an answer is correct, so that it can be applied in the future. Good luck!

Answer 3

x=5

Answer 4

0 = 1 - 2 / ( x - 5)
-1 = - 2/ (x - 5)
-1* (x - 5) = -2
-1x + 5 = -2
-1x = -7
x = 7
QED

Answer 5

the question seems not to be clear enough. I thk the ans is -2