Problems with pre-calculus Rational Equations

[Mariodav94]

Ok, I have some problems with some Rational Equations from my pre-calculus book and somehow I cant seem to be able to do them right as the answer in the book and my answer are different.
Yes I have tried every way of doing it, and yes I have attended my lectures, still we only saw this topic one day so the professor didn't made many examples.

Here are the problems.

20.- 4/((x^2 -1)^2) +1 = 5/(x^2 -1)
The answer in the book is: ( + or - Sqroot of 5 , + or - sqroot of 2) I have no Idea how to get that result, ( I didnt know how to write square root so I wrote sqroot)

the other one is

24.- ( x/(x+1) )^2 +(2x/(x+1)) -51=0
The book answer is -25 +or- sqroot of 13/24 .... The only thing I can get from this is that it can be solved with the quadratic formula but still cant get this result.


I would really appreciate your help as I have partials in a week so I need to understand this at a 100%

 

[Deleted member 4993]

Ok, I have some problems with some Rational Equations from my pre-calculus book and somehow I cant seem to be able to do them right as the answer in the book and my answer are different.
Yes I have tried every way of doing it, and yes I have attended my lectures, still we only saw this topic one day so the professor didn't made many examples.

Here are the problems.

20.- 4/((x^2 -1)^2) +1 = 5/(x^2 -1) ....... Multiply both sides by (x^2 - 1)^2 ..... simplify and expand and solve for the roots of the quadratic
The answer in the book is: ( + or - Sqroot of 5 , + or - sqroot of 2) I have no Idea how to get that result, ( I didnt know how to write square root so I wrote sqroot)

the other one is

24.- ( x/(x+1) )^2 +(2x/(x+1)) -51=0....... Multiply both sides by (x + 1)^2 ..... simplify and expand and solve for the roots of the quadratic
The book answer is -25 +or- sqroot of 13/24 .... The only thing I can get from this is that it can be solved with the quadratic formula but still cant get this result.


I would really appreciate your help as I have partials in a week so I need to understand this at a 100%

.

 

[Mariodav94]

Book answer needs another set of brackets:
(-25 +or- sqrt(13)) / 24 ...and is correct.

Try this: to simplify or shorten process, let k = x + 1
Then the equation becomes:
x^2 / k^2 + 2x / k - 51 = 0

Multiply by k^2:
x^2 + 2xk - 51k^2 = 0

Now substitute back in:
x^2 + 2x(x + 1) - 51(x + 1)(x + 1) = 0

Expand:
x^2 + 2x^2 + 2x - 51(x^2 + 2x + 1) = 0

Simplify and you'll end up with:
48x^2 + 100x + 51 = 0

Now use the quadratic...

Similarly with your other problem: let k = x^2 - 1

Thanks! I really appreciate that, I cant believe how easy it was and I asked for help for something like this, its kind of embarrassing. Still thanks! I will remember to substitute the variables more often to make it easier.