# Thread: Is this Complex Rational Expression right?

1. ## Is this Complex Rational Expression right?

(x+5)(x-2) - (x+5)(x+1)
---------- ----------
(x+5)(x+1) (x+5)(x-2)
--------------------------
(x+5)(x+1) - (x+5)(x-2)
----------- -----------
(x+5)(x-2) (x+5)(x+1)

So I factor them than I multiply times the LCD which (x+5)(x+1)(x-2)

I got this.

(x+5)(x-2)(x-2) - (x+5)(x+1)(x+1)
-----------------------------------
(x+5)(x+1)(x+1) - (x+5)(x-2)(x-2)

Than I subtracted like terms (x+5) which left me with this.

(x-2)(x-2)(x+1)(x+1)
---------------------
(x+1)(x+1)(x-2)(x-2)

I cancel like terms which is everything so I got this

1
--- = 1
1

What do you guys think does that look right?

2. Originally Posted by carlos_gaona_17
(x+5)(x-2) - (x+5)(x+1)
---------- ----------
(x+5)(x+1) (x+5)(x-2)
--------------------------
(x+5)(x+1) - (x+5)(x-2)
----------- -----------
(x+5)(x-2) (x+5)(x+1)

So I factor them than I multiply times the LCD which (x+5)(x+1)(x-2)

I got this.

(x+5)(x-2)(x-2) - (x+5)(x+1)(x+1)
-----------------------------------
(x+5)(x+1)(x+1) - (x+5)(x-2)(x-2)

Than I subtracted like terms (x+5) which left me with this.

(x-2)(x-2)(x+1)(x+1)
---------------------
(x+1)(x+1)(x-2)(x-2)

I cancel like terms which is everything so I got this

1
--- = 1
1

What do you guys think does that look right?
Red part has error above
It should be
(x-2)(x-2) - (x+1)(x+1)
---------------------
(x+1)(x+1)(x-2)(x-2)

(x-2)(x-2) - (x+1)(x+1)
= ---------------------
(x+1)(x+1)(x-2)(x-2)

$\displaystyle 3/ (x+1)(x+1)(x-2)(x-2)$

= $\displaystyle 3/(x+1)^2(x-2)^2$

3. Where did you get that 3 from?

4. Originally Posted by carlos_gaona_17
Where did you get that 3 from?
You can't cancel across addition or subtraction signs.

So to simplify the top you'd have to expand and collect like terms.

I however, get as my final answer

$\displaystyle \frac{-6x + 3}{(x - 2)^2(x + 1)^2}$.

5. carlos_gaona_17 you just messed up in typing the question.
please use Latex while typing the mathematical expressions in this forum.

If you take LCM, your expression will reduce to
$\displaystyle ((x - 2)^2 - (x + 1)^2))/((x + 1)^2 - (x - 2)^2)$
= -1