Solve the Fractional Equation: Unveiling 36/4x + 35/7 - 81/9x = 16/8 + 45/5x - 38/19

To solve the problem, we'll follow these steps:

• Step 1: Simplify each fraction in the equation.
• Step 2: Combine like terms involving $x$ on one side of the equation and constants on the other.
• Step 3: Solve the simplified equation for $x$.

Let's work through each step together:

Step 1: Simplify each fraction:

• $\frac{36}{4} = 9$,
• $\frac{35}{7} = 5$,
• $\frac{81}{9} = 9$,
• $\frac{16}{8} = 2$,
• $\frac{45}{5} = 9$,
• $\frac{38}{19} = 2$.

With these simplifications, our equation becomes:

$9x + 5 - 9x = 2 + 9x - 2$.

Step 2: Combine like terms.

• The terms $9x$ and $-9x$ cancel out on the left, so we have:
• $5 = 2 + 9x - 2$.
• Simplify the right side: $5 = 9x$.

Step 3: Solve for $x$:

$5 = 9x$

Divide both sides by $9$:

$x = \frac{5}{9}$.

Therefore, the solution to the equation is $x = \frac{5}{9}$.