SOLUTION: I AM STUCK WITH THIS ONE AND IT IS MOST OFTEN ASKED SO PLEASE HELP ME !! 2 ( x-1 / x+3 ) -7 ( x+3 / x-1 ) = 5

Question 846547: I AM STUCK WITH THIS ONE AND IT IS MOST OFTEN ASKED SO PLEASE HELP ME !! 2 ( x-1 / x+3 ) -7 ( x+3 / x-1 ) = 5
Found 2 solutions by Fombitz, josh_jordan:
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
Multiply both sides by (x-1)(x+3).

Two solutions:

and

Answer by josh_jordan(263) (Show Source): You can put this solution on YOUR website!

The first thing we need to do is multiply 2 by (x - 1) and multiply 7 by (x + 3):

Next, we need to subtract the remaining fractions on the left side of the equation. We do this by multiplying (2x - 2) by (x - 1) and multiplying (7x + 21) by (x + 3) and setting this result in the numerator and setting (x + 3)(x - 1) in the denominator:

----->

Next, after distributing the minus sign to (7x^2 + 42x + 63), combine all of the terms in the numerator and set that above the denominator:

----->

Next, since this single fraction is set equal to a number, we will cross-multiply the numerator in the fraction, by 1, since 5 = 5/1, and multiply the denominator in the fraction by 5:

----->

----->

Now, since this is a quadratic equation, we need to move all of the terms to one side of the equation and set the other side of the equation equal to 0:

Combining like terms gives us:

Now we have this in quadratic form. Let's make this equation easier to factor by factoring out 2, giving us:

Now, this is easily factorable:

We can discard the 2 we factored out, and set each of our factors equal to zero to find our x's:

----->

----->

AND

----->

We now have solved for x.

x = -1 and -23/5

You need to verify both of these values of x work by plugging each value of x into the original equation. Both, in fact, do work, so

x = -1 and -23/5

RELATED QUESTIONS
I am stuck again. I am not sure how to simplify this one with the exponent in it... (answered by Heretohelpya!)
Hello! My name is Salem and I am a concurrently enrolled student at Carl Albert State... (answered by rapaljer)
Could you pls, help me with this? Complete this linear function table: ( x , (answered by vleith)
I have been asked to solve the equations simultaneously, and i believe one of them to be... (answered by venugopalramana)
i am currently working on the carnegie learning disc. i have submitted parts of the... (answered by venugopalramana,funmath)
Can you please help me solve this radical equaqtion? {{{sqrt(x-1)+x=3}}} This problem... (answered by Edwin McCravy)
We are doing inverses in class and I am stuck on this one problem. Can you help me? It (answered by fractalier)
I need help with this one. I cannot seem to understand it. I have tried for about an hour (answered by tutor_paul)
can you please help me with this problem?? i really need your help!! thank you so much (answered by jim_thompson5910)