SOLUTION: Change the rational equation to quadratic form and solve it by the most efficient method. (Enter your answers as a comma-separated list.) x(2x + 1)/ x-4= 36/x-4 I keep ge

Algebra ->  College  -> Linear Algebra -> SOLUTION: Change the rational equation to quadratic form and solve it by the most efficient method. (Enter your answers as a comma-separated list.) x(2x + 1)/ x-4= 36/x-4 I keep ge      Log On


   

Question 707909: Change the rational equation to quadratic form and solve it by the most efficient method. (Enter your answers as a comma-separated list.)

x(2x + 1)/ x-4= 36/x-4

I keep getting the answers 4 and -9/2 but its not right. I have tried multiplying both fractions by x-4 to get rid of them. then from there i have done quadratic formula and completing the square and i still get the same answers
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
If the problem is %28x%282x%2B1%29%29%2F%28x-4%29+=+36%2F%28x-4%29, then you can multiply both sides by x-4 to get x%282x%2B1%29+=+36

If you solve that for x, you will get 4, -9/2 ... BUT...these are the solutions to x%282x%2B1%29+=+36 and NOT the original equation.

This is why you must check any and all possible answers you get in the original equation.

Notice that if x = 4, then x - 4 is equal to zero. But x-4 is a denominator and if that is zero, then you have a division by zero error. To avoid this division by zero error, you make the restriction that x%3C%3E4

So x = 4 is NOT a solution

This just leaves the only solution to be -9/2