SOLUTION: This problem is from Prentice Hall's Algebra 2 with trigonometry. (2x + 3)/(x-1) = 10/(x^2-1) + (2x-3)/(x+1) I am a mom helping several of the students with their math homework.

Algebra ->  Equations -> SOLUTION: This problem is from Prentice Hall's Algebra 2 with trigonometry. (2x + 3)/(x-1) = 10/(x^2-1) + (2x-3)/(x+1) I am a mom helping several of the students with their math homework.      Log On


   

Question 376609: This problem is from Prentice Hall's Algebra 2 with trigonometry. (2x + 3)/(x-1) = 10/(x^2-1) + (2x-3)/(x+1) I am a mom helping several of the students with their math homework. However, I got the same answer they did on this problem but the book says there is no solution. We all got x = 1. What are we doing wrong. Thanks so much Debbie
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
When you multiply every term by the LCD x%5E2-1, you get the equation


%282x+%2B+3%29%28x%2B1%29=10%2B%282x-3%29%28x-1%29



If you solve the equation above, you get the solution x=1. However, you must check your solution by plugging it into the original equation.


This is where the problem lies. If you plug in x=1 into %282x+%2B+3%29%2F%28x-1%29+=+10%2F%28x%5E2-1%29+%2B+%282x-3%29%2F%28x%2B1%29+, you get


%282%281%29+%2B+3%29%2F%281-1%29+=+10%2F%281%5E2-1%29+%2B+%282%281%29-3%29%2F%281%2B1%29+


which then becomes


5%2F0+=+10%2F0+%2B+-1%2F2+


Since you CANNOT divide by zero, this means that x=1 is NOT in the domain. So this means that x%3C%3E1


This then means that x=1 is NOT a solution.


So there are no solutions.


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim