https://file.aiquickdraw.com/mathbot/file/1725432985893qu5t97dj.jpg

The expression in the image is:

\[
\frac{2x^2}{x^2 + 2x - 3}
\]

To simplify or analyze this expression, let's first factorize the denominator and check if any common factors can be canceled out.

### Step 1: Factorize the Denominator

The denominator is a quadratic expression:

\[
x^2 + 2x - 3
\]

We need to find two numbers that multiply to \(-3\) (constant term) and add up to \(2\) (coefficient of \(x\)). These numbers are \(3\) and \(-1\). Thus, we can factor the quadratic as:

\[
x^2 + 2x - 3 = (x + 3)(x - 1)
\]

### Step 2: Rewrite the Expression

Now, the given expression becomes:

\[
\frac{2x^2}{(x + 3)(x - 1)}
\]

### Step 3: Simplify if Possible

There are no common factors in the numerator and the denominator that can be canceled. Therefore, the expression is already in its simplest form.

### Final Answer

\[
\frac{2x^2}{(x + 3)(x - 1)}
\]

Would you like a detailed explanation of any specific step, or do you have any questions?

### Related Questions:

1. How do you find the roots of a quadratic equation?
2. What is the method to factorize a quadratic expression?
3. How do you determine the domain of a rational function?
4. What is the difference between simplifying and factoring an expression?
5. How do you handle division by zero in rational expressions?

**Tip:** When simplifying rational expressions, always check for common factors that can be canceled after factoring the numerator and the denominator.

Simplify the expression 2x^2 / (x^2 + 2x - 3).

This page provides a step-by-step guide on simplifying the rational expression 2x^2 / (x^2 + 2x - 3). The solution involves factoring the quadratic expression and checking for common factors. Ideal for students in Grades 9-10.

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