1. **State the problem:** Solve the equation with fractions and variable $x$: $$\frac{a}{b} x + \frac{c}{d} = \frac{e}{f} x + \frac{g}{h}$$ where $a,b,c,d,e,f,g,h$ are the numerators and denominators of the fractions (unknown in the problem). 2. **Formula and rules:** To solve for $x$, first get all terms with $x$ on one side and constants on the other. 3. **Step 1: Move terms involving $x$ to one side:** $$\frac{a}{b} x - \frac{e}{f} x = \frac{g}{h} - \frac{c}{d}$$ 4. **Step 2: Factor out $x$ on the left:** $$x \left( \frac{a}{b} - \frac{e}{f} \right) = \frac{g}{h} - \frac{c}{d}$$ 5. **Step 3: Find common denominators and subtract fractions:** $$\frac{a}{b} - \frac{e}{f} = \frac{af - eb}{bf}$$ $$\frac{g}{h} - \frac{c}{d} = \frac{gd - ch}{hd}$$ 6. **Step 4: Solve for $x$ by dividing both sides:** $$x = \frac{\frac{gd - ch}{hd}}{\frac{af - eb}{bf}}$$ 7. **Step 5: Simplify the complex fraction:** $$x = \frac{gd - ch}{hd} \times \frac{bf}{af - eb}$$ 8. **Final answer:** $$x = \frac{(gd - ch)(bf)}{(hd)(af - eb)}$$ This is the general solution for $x$ in terms of the numerators and denominators of the fractions. If you provide the specific numbers for the fractions, I can compute the exact value of $x$.