Solve the equation- complex rational expressions

Question

x-3      x=5      1

----  = ----- + ----

x²            5x²        5x

Answer 1

First, you must find a common denominator. I would use 5x² for this, since the second fraction already has that denominator, and everything can be easily changed to 5x².

So, in the first portion, on the left side of the equation, we have to get the bottom to be 5x².

5(x-3)  = x-5   + x(1)  

5(x²⁾         5x²       x(5x) 

I apologize for my poor formatting. Please bare with me. So, in order to get the first fraction tobe 5x² on the bottom, we need to multiply the fraction by 5/5. For the third fraction to change, we have to multiply it by x/x. This way, we are still multiplying by one, so we are not actually changing the equation; we are only changing how it looks. Similar to the way that 2/4 still equals 1/2, even though it looks different. This leads the equation to be:

5x-15 = x-5  +  x  

5x²       5x²     5x²

Now, we just solve for x.

5x-15=5x²(x-5+x)

   5x²

5x-15=x-5+x

5x-15=2x-5

3x=10

x=10/3.