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

Question

Look at the following function:

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

What is the domain of the function?

00:00 Does the function have a domain? And if so, what is it?

00:03 To find the domain, remember that division by 0 is not allowed

00:07 So let's see what solution zeros the denominator

00:11 Let's isolate X

00:23 And this is the solution to the question

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 $x\ne\frac{3}{5}$ .

$x\ne\frac{3}{5}$