Write the polynomial expression in the simplest form: x^2 - 9/x^2 - 4 * 4x - 8/12x + 26
The simplest form of the polynomial expression is:
(x^2 - 9)/(x^2 - 4) - (4x - 8)/(12x) + 26
To simplify the given polynomial expression, let's break it down into separate fractions:
x^2 - 9 / x^2 - 4 * 4x - 8 / 12x + 26
First, let's factor the numerator and denominator separately:
(x - 3)(x + 3) / (x - 2)(x + 2) * 4(x - 2) / 4x(3) + 26
Now, let's cancel out like terms between the numerator and denominator:
(x - 3) / (x + 2) * 1 / (3) + 26
Simplifying the expression further, we get:
(x - 3) / (x + 2) * 1/3 + 26
Therefore, the simplified polynomial expression is:
(x - 3)/(3(x + 2)) + 26
To simplify the given polynomial expression, we'll start by factoring the numerator and denominator separately.
The numerator, x^2 - 9, is a difference of squares and can be factored as (x + 3)(x - 3).
The first term of the denominator, x^2 - 4, is also a difference of squares and can be factored as (x + 2)(x - 2).
The second term of the denominator, 4x - 8, can be simplified by factoring out the greatest common factor, which is 4. We get 4(x - 2).
The third term of the denominator, 12x + 26, can be simplified by factoring out the greatest common factor, which is 2. We get 2(6x + 13).
Now, we can rewrite the original expression with the factored forms:
(x^2 - 9) / (x^2 - 4 * 4x - 8 / 12x + 26) = (x + 3)(x - 3) / ((x + 2)(x - 2) * 4(x - 2) / 2(6x + 13))
Next, we can cancel out common factors between the numerator and the denominator.
The (x - 2) terms cancel out in the numerator and the denominator.
(x + 3)(x - 3) / ((x + 2)(4(6x + 13))
Finally, we can simplify the expression further by multiplying the remaining factors:
(x + 3)(x - 3) / (4(x + 2)(6x + 13))
This is the simplified form of the given polynomial expression.