Determine the Domain: Tackle (10x-3)/(5x-3) in Rational Function Analysis

Look at the following function:

$\frac{10x-3}{5x-3}$

What is the domain of the function?

To find the domain of the function $\frac{10x-3}{5x-3}$, we'll follow these steps:

• Identify the denominator: $B(x) = 5x - 3$.
• Set the denominator equal to zero: $5x - 3 = 0$.
• Solve for $x$: Add 3 to both sides, getting $5x = 3$. Then, divide by 5: $x = \frac{3}{5}$.
• Conclude that the domain is all real numbers except $x = \frac{3}{5}$, since this makes the denominator zero.

Therefore, the domain of the function is all real numbers except $x\ne\frac{3}{5}$.