Question

36x^2-1 ________- скоротити дріб 36x^2-12+1

Answer 1

$\frac{(6x)^2 - 1}{(6x)^2 - 12x + 1} = \frac{(6x -1)(6x + 1)}{(6x-1)(6x-1)} = \frac{(6x + 1)}{(6x - 1)}$

Answer 2

To simplify the fraction (rational expression) 36x^2 - 1 / (36x^2 - 12 + 1), we need to factor the numerator and denominator and then cancel out common factors.

1. Factor the numerator and denominator: Numerator: 36x^2 - 1 can be factored as (6x)^2 - 1^2, which is a difference of squares. So, the numerator becomes (6x - 1)(6x + 1). Denominator: 36x^2 - 12 + 1 does not factor further.

2. Now, rewrite the fraction with factored terms: (36x^2 - 1) / (36x^2 - 12 + 1) = [(6x - 1)(6x + 1)] / (36x^2 - 12 + 1)

3. Simplify the fraction by canceling common factors: Since there are no common factors between the numerator and denominator, the expression is already in its simplest form.

Therefore, the simplified expression is: (6x - 1)(6x + 1) / (36x^2 - 12 + 1).