# Domain of One Variable Function – Rational function – Exercise 5730

Exercise

Determine the domain of the function:

$$y=\frac{x^2+3}{2x-1}$$

$$x\neq \frac{1}{2}$$

Solution

Let’s find the domain of the function:

$$y=\frac{x^2+3}{2x-1}$$

It is a rational function (a fraction of polynomials). Because there is a denominator, the denominator must be different from zero:

$$2x-1\neq 0$$

To get the final answer, isolate x on one side:

$$2x\neq 1$$

$$x\neq \frac{1}{2}$$

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