(2x-3)(root X-1)/2x^2+x-3

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Jun 07, 2024

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Simplifying the Algebraic Expression: (2x-3)(root x-1)/2x^2+x-3

In this article, we will explore the simplification of the algebraic expression (2x-3)(root x-1)/2x^2+x-3. This expression involves a combination of multiplication, roots, and division, making it a challenging problem to simplify. Let's break it down step by step.

Simplifying the Numerator

The numerator of the expression is (2x-3)(root x-1). To simplify this, we need to follow the order of operations (PEMDAS).

First, we will simplify the expression inside the parentheses:

(2x-3)(root x-1) = 2x(root x) - 3(root x) - 2x + 3

Now, we will simplify each term:

• 2x(root x) = 2x√x (since root x means the square root of x)
• -3(root x) = -3√x
• -2x + 3 = -2x + 3 (no simplification needed)

So, the simplified numerator is:

2x√x - 3√x - 2x + 3

Simplifying the Denominator

The denominator of the expression is 2x^2+x-3. This is already in simplest form, so we can move on to the next step.

Simplifying the Entire Expression

Now, we can simplify the entire expression by dividing the numerator by the denominator:

(2x√x - 3√x - 2x + 3) / (2x^2 + x - 3)

To simplify this, we can try to factor the numerator and denominator, but it's not possible in this case. Therefore, the simplified expression is:

(2x√x - 3√x - 2x + 3) / (2x^2 + x - 3)

Conclusion

In conclusion, the simplified form of the algebraic expression (2x-3)(root x-1)/2x^2+x-3 is (2x√x - 3√x - 2x + 3) / (2x^2 + x - 3). This expression still contains a radical, but it is in its simplest form.