%2F(2x%5E2%2Bx-3).jpeg "(x-1)/(2x^2+x-3)")
Rational Expression: (x-1) / (2x^2 + x - 3)
In this article, we will explore the rational expression (x-1) / (2x^2 + x - 3), its properties, and how to simplify it.
Definition
A rational expression is an expression that can be written as the ratio of two polynomials. In this case, our rational expression is (x-1) / (2x^2 + x - 3), where the numerator is x-1 and the denominator is 2x^2 + x - 3.
Properties
Domain
The domain of the expression (x-1) / (2x^2 + x - 3) is all real numbers except those that make the denominator zero. To find the domain, we set the denominator equal to zero and solve for x.
2x^2 + x - 3 = 0
Factoring the quadratic expression, we get:
(2x - 3)(x + 1) = 0
This gives us two possible values for x: x = 3/2 and x = -1. Therefore, the domain of the expression is all real numbers except x = 3/2 and x = -1.
Simplification
To simplify the expression, we can try to factor the numerator and denominator and cancel out any common factors.
(x-1) / (2x^2 + x - 3) = ?
Unfortunately, it is not possible to simplify this expression further without knowing more about the context in which it is being used.
Graph
The graph of the expression (x-1) / (2x^2 + x - 3) is a non-linear rational function. The graph has asymptotes at x = 3/2 and x = -1, which are the values that make the denominator zero.
Conclusion
In conclusion, we have explored the rational expression (x-1) / (2x^2 + x - 3), its properties, and how to simplify it. We have also discussed its domain and graph. Understanding rational expressions is an important part of algebra and is used in many real-world applications.
