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
(sinceroot 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.