Solving rational equations

[czagara]

I have been working on this problem for over an hour now and I cannot seem to come up with the right answer.
Please help!

1. (x-2) / (x+3) - (x-1) / (x+4) = (x) / (x+3) + (x-1) / x^x +7x +12

 

[mmm4444bot]

(x-2) / (x+3) - (x-1) / (x+4) = (x) / (x+3) + (x-1) / x^x + 7x +12 Is this term supposed to be x^2 ?

If the denominator noted above is supposed to be x^2 + 7x+ 12, then factor it.

Multiply both sides of the equation by the GCD; this will clear the fractions.

You worked for over an hour, but you did not show us what you tried.

If you need more help, then please show your work.

 

[Denis]

1. (x-2) / (x+3) - (x-1) / (x+4) = (x) / (x+3) + (x-1) / x^x +7x +12

Zza Zza, all looks fine (posting wise) except last term:
is it really what you posted; I think it's x^2 +7x +12;
plus it should be bracketed, right? Like (x-1) / (x^2 +7x +12).

 

[czagara]

yes that is how its supposed to written X^2. x^2 means x squared right?

 

[czagara]

This is what I have come up with so far...

LCD: is (x+3)(x+4)

If you mulitply the top and bottom of all the fractions you would get,

(X^2 -8) - (-X^2+3)=(X^2 +4X)+x-1

The X^2 cancel out and you are left with X^2 + 5X - 4=0

I have no idea what to do from here?

My book said the answer is -1

 

[Denis]

This is what I have come up with so far...
LCD: is (x+3)(x+4)
If you mulitply the top and bottom of all the fractions you would get,
(X^2 -8) - (-X^2+3)=(X^2 +4X)+x-1
The X^2 cancel out and you are left with X^2 + 5X - 4=0
I have no idea what to do from here?
My book said the answer is -1

Good work Zza Zza!
Close: should be x^2 + 5x + 4 = 0 (check your work; must have a sign error somewhere).
Factoring that: (x + 4)(x + 1) = 0
So x = -4 or x = -1

x = -4 is out, since x + 4 is a divisor in one of the terms; division by 0 is illegal;
so x = -1

 

[mmm4444bot]

… If you [multiply] the top and bottom of all the fractions you would get, When trying to "clear the fractions", we do not multiply "top and bottom".

We multiply both sides of the equation by the GFD: (x + 3)(x + 4)

Doing this will clear all of the algebraic fractions.

(X^2 -8) - (-X^2+3)=(X^2 +4X)+x-1 This line is wrong.

(x + 4)(x - 2) does not equal x^2 - 8.

(x + 3)(x - 1) does not equal x^2 - 3.

It looks to me like you need to review FOIL (i.e., how to properly multiply two binomials).

Multiplying both sides of the given equation by the GCD gives the following.

(x + 4)(x - 2) - (x + 3)(x - 1) = (x + 4)(x) + x - 1

x^2 + 2x - 8 - (x^2 + 2x - 3) = x^2 + 4x + x - 1

Journey onward!