Simplify (6x(x+1))/(x-1)
The problem is asking to perform a simplification process on the algebraic expression (6x(x+1))/(x-1). This involves applying arithmetic operations and algebraic rules such as the distributive property to combine and reduce the terms within the expression to their simplest form. The aim is to rewrite the expression in a way that is easier to understand or analyze, ideally with fewer terms or lower degree polynomials, while maintaining the mathematical equivalence to the original expression.
$\frac{6 x \left(\right. x + 1 \left.\right)}{x - 1}$
Answer
Solution:
Step 1:
First, we have the given expression:
$$\frac{6x(x + 1)}{x - 1}$$
Step 2:
We need to simplify the expression by performing the multiplication in the numerator:
$$\frac{6x^2 + 6x}{x - 1}$$
Step 3:
The expression is already simplified as much as possible, since the numerator and denominator do not share any common factors other than 1. Therefore, the simplified form of the expression remains:
$$\frac{6x^2 + 6x}{x - 1}$$
Knowledge Notes:
To simplify a rational expression, follow these steps:
Expand the Numerator and Denominator: Multiply out any factors in the numerator and denominator to see if they can be simplified.
Factorize: Attempt to factor both the numerator and the denominator. This step is crucial for identifying common factors that can be canceled out.
Cancel Common Factors: If the numerator and denominator share any common factors (other than 1), you can simplify the expression by canceling them out.
Check for Further Simplification: Ensure that the expression is in its simplest form by checking for any additional common factors or terms that can be combined.
In the given problem, the numerator is already in a factored form, and after expanding, we find that there are no common factors with the denominator. Therefore, the expression is in its simplest form.
