To solve the equation ((x)/(5x+10)) + ((x-3)/(x+2)) = (7)/(5), you correctly multiplied both sides of the equation by 5 to eliminate the denominator in the first term:
(x/(x+2)) + (5x-15/(x+2)) = 7
Next, you multiplied both sides of the equation by (x+2) to eliminate the denominator in the second term:
x + 5x - 15 = 7(x+2)
Now, combine like terms:
6x - 15 = 7x + 14
Subtract 6x from both sides:
-15 = x + 14
Finally, subtract 14 from both sides:
x = -29
So, the solution to the equation is x = -29.
Regarding your previous attempts, it's possible that there was a mistake made in simplifying expressions or rearranging terms, which led to different results. It's always a good idea to double-check your work and review any mistakes to ensure accuracy.