Question 6600: Dear Sir/Madam,
I am confronted with the following problem:
"Solve the equation.
3/(2x-5) + 2/(2x+5) = (10x + 5)/(4x^2 - 25)"
When you work out the left side of the equation (i.e. the addition) you get exactly the same thing as on the right side, so it is just like saying 1 = 1 is it not? I don't understand why the answer is all real numbers except +-5/2. Can you help me please?
Thanks in advance.
Regards,
-Mike
Answer by prince_abubu(198)   (Show Source):
You can put this solution on YOUR website! When you end up with 1 = 1 at the end, or a number equals itself after going through algebraic manipulations, the solution is the set of all real numbers.
However, in this case, you have 2x-5 and 2x+5 in the denominators. Remember that the denominator can NEVER be zero. In this example, the values 5/2 and -5/2 will make the denominator zero. The solution then would be the set of real numbers except +-5/2.
Just in case it might look like I skipped steps, We'll have the equations 2x - 5 = 0 AND 2x + 5 = 0. We are NOT solving for x here. We are just setting the denominators to equal zero to find out what x values make the denominators zero. When you "solve for x" (that is, to find that troublemaker x value), you're finding the value or values that will make your equation NOT WORK FOR SURE.
|
|
|
