# LCD in Rational Expressions

• Sep 21st 2007, 04:04 PM
some_nerdy_guy
LCD in Rational Expressions
Can some one help me find the LCD of this problem? I don't see it but apparently there is, considering the answer is -(37/18) and not "No solution."

(2/5x+5)-(3/[x^2]-4)=(4/x-1)

The textbook we use gives the WORST examples (they're way too simple to apply to the more complex problems.)
• Sep 21st 2007, 04:23 PM
TKHunny
You just have to factor all the denominators and have a look at it.

5x+5 = 5(x+1)

x^2 - 4 = (x+2)(x-2)

Looks to me like 5(x+1)(x-1)(x+2)(x-2) will cover it.

Note: Fix your notation. These two expressions are NOT the same.

2/5x+5

2/(5x+5)

You tell me how they are different and whether it matters.
• Sep 21st 2007, 09:46 PM
ticbol
Quote:

Originally Posted by some_nerdy_guy
Can some one help me find the LCD of this problem? I don't see it but apparently there is, considering the answer is -(37/18) and not "No solution."

(2/5x+5)-(3/[x^2]-4)=(4/x-1)

The textbook we use gives the WORST examples (they're way too simple to apply to the more complex problems.)

Even if not considering the the answer, one would suspect that the (x^2 -4) should be (x^2 -1). Because the problem is asking for the LCD and there are (x-1) and (x+1) factors among the 3 denominators.

Espescially so when one considers the anwser.
(2 / 5x+5) -(3 / x^2 -1) = (4 / x-1)

The LCD is 5(x^2 -1), or 5(x+1)(x-1).

Multiply both sides by 5(x^2 -1),
2(x-1) -3(5) = 4(5)(x+1)
2x -2 -15 = 20x +20
2x -20x = 20 +2 +15
-18x = 37
x = -37/18