30. Solve $\frac{3}{x+3}+\frac{2}{2 x-6}=\frac{7}{8}$ for $x$.

Step 1 ：Solve the equation \(\frac{3}{x+3}+\frac{2}{2x-6}=\frac{7}{8}\) for \(x\).

Step 2 ：The equation is a rational equation. To solve it, we will first clear the fractions by multiplying each term by the least common multiple (LCM) of the denominators. The LCM of \(x+3\), \(2x-6\), and \(8\) is \(8(x+3)(2x-6)\). After clearing the fractions, we will simplify the equation and solve for \(x\).

Step 3 ：The simplified equation is \(\frac{2(2x - 3)}{x^2 - 9} = 0.875\).

Step 4 ：Solving this equation gives two solutions for \(x\), which are \(x = -0.428571428571429\) and \(x = 5.00000000000000\).

Step 5 ：However, we need to check if these solutions are valid by substituting them back into the original equation. If the original equation holds true with these values, then they are the valid solutions.

Step 6 ：Substituting the solutions back into the original equation, we find that only \(x = 5.00000000000000\) is a valid solution.

Step 7 ：Final Answer: The valid solution for the equation \(\frac{3}{x+3}+\frac{2}{2x-6}=\frac{7}{8}\) is \(x = \boxed{5}\).