what is the value of x in given rational (x-1)/(2x+3)=0?

To solve the equation \(\frac{x-1}{2x+3} = 0\), we need to find the value of \(x\) that makes the numerator equal to zero, because a fraction equals zero only when its numerator is zero (and the denominator is non-zero).

Given:

\[
\frac{x-1}{2x+3} = 0
\]

Set the numerator equal to zero:

\[
x - 1 = 0
\]

Solve for \(x\):

\[
x = 1
\]

So, the value of \(x\) is \(1\).

**Final answer: \(x = 1\)**

Do you want more details or have any questions about this solution? Here are some related questions to explore:

1. What is the value of \(x\) in \(\frac{2x - 5}{x + 4} = 0\)?
2. How do you solve the rational equation \(\frac{x^2 - 4}{3x + 2} = 0\)?
3. What happens if the denominator of a rational equation is zero?
4. How do you find the domain of the function \(f(x) = \frac{x - 2}{x^2 - 9}\)?
5. What is the difference between solving a linear equation and a rational equation?

**Tip:** When solving rational equations, always check if the solution makes the denominator zero. If it does, the solution is not valid.

Learn how to solve the rational equation (x-1)/(2x+3)=0 with a step-by-step solution. Understand the concept of rational equations and how to isolate variables to find solutions. Suitable for high school students.

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