Question 85440
Multiply everything by the LCD of the fractions, which is 5(x + 2)  [put the 5x + 10 in factored form to make it easier]:

5(x + 2)({{{x/(5x + 10)}}} + {{{(x - 3)/(x + 2)}}} = {{{7/5}}}

The denominators of each fraction now cancel out:

x + 5(x - 3) = 7(x + 2)

Apply the distributive property:

x + 5x - 15 = 7x + 14

Combine like terms:

6x - 15 = 7x + 14

Get variables to one side and constants to the other side:

6x - 7x = 14 + 15  [subtract 7x from both sides and add 15 to both sides]

-x = 29

Divide both sides by -1:

x = -29

Check for extraneous solutions [denominaotrs can't = 0]:

x + 2 = -29 + 2 = -27. Since this isn't = 0, the solution x = -29 is good