What is the solution to the rational equation 3 over 2 - 1 over x plus 5 = negative 2 over 2x plus 10 ?

Question

What is the solution to the rational equation 3 over 2 - 1 over x plus 5 =  negative 2 over 2x plus 10 ?

doc.brown · Answer

Let me just write it out first,
$$\frac{3}{2}-\frac{1}{x+5}=\frac{-2}{2x+10}$$

doc.brown · Answer

Could 2x+10 be a common denominator?

anonymous · Answer

@doc.brown  These are the options given:
 x = -5

 x = -5 over 2

 x = 5

 No solution

doc.brown · Answer

This is how I did it
$$\frac{x+10}{x+10}(\frac{3}{2})-\frac{2}{2}(\frac{1}{x+5})=\frac{-2}{2x+10}$$$$\frac{3x+10}{2x+10}-\frac{2}{2x+10}=\frac{-2}{2x+10}$$

anonymous · Answer

@doc.brown  So out of those four options which one do you think it would be then? Still kind of confused on how to get the answer?

doc.brown · Answer

Ok, watch what happens when you add 2/(2x+10) to both sides$$\frac{3x+10}{2x+10}-\frac{2}{x+10} + \frac{2}{x+10}=\frac{-2}{2x+10} +\frac{2}{x+10}$$$$\frac{3x+10}{2x+10}=0$$