Let's solve the given equations step by step.

The given equations are:
1. \(\frac{30}{x} - \frac{45}{x} + 4 = \frac{130}{x}\)
2. \(\frac{45}{x+4} = 1\)

### Solving the First Equation

First, simplify the left-hand side of the first equation:
\[
\frac{30}{x} - \frac{45}{x} + 4 = \frac{130}{x}
\]

Combine the fractions:
\[
\frac{30 - 45}{x} + 4 = \frac{130}{x}
\]

Simplify the numerator:
\[
\frac{-15}{x} + 4 = \frac{130}{x}
\]

To eliminate the fractions, multiply every term by \(x\):
\[
-15 + 4x = 130
\]

Solve for \(x\):
\[
4x = 130 + 15
\]
\[
4x = 145
\]
\[
x = \frac{145}{4}
\]
\[
x = 36.25
\]

### Solving the Second Equation

Now, solve the second equation:
\[
\frac{45}{x+4} = 1
\]

Multiply both sides by \(x + 4\) to eliminate the fraction:
\[
45 = x + 4
\]

Solve for \(x\):
\[
x = 45 - 4
\]
\[
x = 41
\]

### Summary

The solutions to the equations are:
1. \(x = 36.25\) from the first equation.
2. \(x = 41\) from the second equation.

These solutions are independent and specific to their respective equations.