Math Help - raftional expression?

1. raftional expression?

x2-x-12 . 3+x
x2-9 4-x

ans (x-4)(3+X)
(X-3)(4-X)

THERE IN THE BOOK IS (3+X)
(X-3)

2. Re: raftional expression?

Originally Posted by zbest1966
THERE IN THE BOOK IS (3+X)
(X-3)
Note that $(4-x) = -(x-4)$.

In general, $(a-b)=-(b-a)$.

Edit: I didn't look too closely at the book's answer, but the other two posters are correct when they say that it is wrong.

3. Re: raftional expression?

Originally Posted by zbest1966
x2-x-12 . 3+x
x2-9 4-x

ans (x-4)(3+X)
(X-3)(4-X)

THERE IN THE BOOK IS (3+X)
(X-3)
\displaystyle \begin{align*} \frac{x^2 - x - 12}{x^2 - 9} \cdot \frac{3 + x}{4 - x} &= \frac{(x - 4)(x + 3)}{(x - 3)(x + 3)}\cdot \frac{3 + x}{4 - x} \\ &= \frac{-(4 - x)(x + 3)(3 + x)}{(x - 3)(x + 3)(4 - x)} \\ &= \frac{-(3+x)}{x - 3} \end{align*}

4. Re: raftional expression?

Originally Posted by zbest1966
x2-x-12 . 3+x
x2-9 4-x

ans (x-4)(3+X)
(X-3)(4-X)

THERE IN THE BOOK IS (3+X)
(X-3)
I disagree the answer in the textbook.

It should be $\frac{3+x}{3-x}$.

5. Re: raftional expression?

if you a negative on the top you must put a negative on the bottom.

6. Re: raftional expression?

Originally Posted by zbest1966
if you a negative on the top you must put a negative on the bottom.
Not true. What I have written is correct, I've just written \displaystyle \begin{align*} x - 4 = -(4 - x) \end{align*} so that you have a common factor you can cancel.