How to get -1 for the answer here? I keep getting positive 1!

The math problem is:

Simplify the rational expression

x-7
-----
7-x

First we notice that the numerator is exactly opposite the denominator, which of course means that the denominator is exactly opposite the numerator...

so...multiply either the numerator or the denominator (but not both) by negative 1.

x-7
-----
7-x

equals

1(x-7)
---------
-1(7-x)

then that equals

x-7
------
-7+x

which is the same thing as

x-7
------
x-7

And then HERE'S where my question is:

I simplify the above solution and I arrive at the result of positive 1.

But the correct answer according to my class is negative 1.

How to get negative 1 from

x-7
-----
x-7

?????????????

x - 7
-------
7 - x

x - 7
----------- {switched bottom around so that x is first}
-x + 7

x - 7
------------- {factored -1 out of bottom}
-1(x - 7)

= -1 {cancelled x - 7 on top and bottom}

http://www.algebrahouse.com

Well, you actually committed a mistake in your formula. Anyway, here's mine:

Given:

(x - 7) / (7 - x) right?

Consider the numerator. If we take out -1 from it, it'll be:

-1(7 - x)

Isn't it that -1(7 - x) = (x - 7)

Do the distribtution and see that we are actually right.

So substituting this to the given:

-1(7 - x) / (7 - x)

And there we have it, we'll just have to cancel the (7 - x) which is present in both numerator and denominator.

And we'll have, of course, an answer of -1.

That's it. =)

You are going round in circles.
First look at the numerator and the denominator
(x - 7) = -(7 - x)
so (x-7)/(7-x) = -(7 -x)/(7-x) = -1

At the beginning, you multiplied the whole problem by -1, so you have to divide by -1 at the end so you don't change the problem. 1 / -1 = -1.

You're forgetting that you multiplied by -1 and you can't do that.

(x-7)/(7-x) = -(7-x)/(7-x) = -1

  x − 7 = - (7 − x) = - 7 + x = x − 7

and so ...

 (x − 7) ⁄ (7 − x) = - (7 − x) ⁄ (7 − x) = -1

x-7
----- =
x-7

-(7-x)
--------
(x-7)

= -1