Write the polynomial expression in the simplest form, x^2 - 9/x^2 - 4 * 4x - 8/12x + 26

Answer 1

The polynomial expression is:

(x^2 - 9) / (x^2 - 4) * (4x - 8) / (12x + 26)

First, let's simplify the expression inside the first parentheses:

(x^2 - 3^2)

This is a difference of squares, which can be factored as:

(x - 3)(x + 3)

Similarly, let's simplify the expression inside the second parentheses:

(4x - 8)

This expression can be factored out a common factor of 4:

4(x - 2)

Lastly, let's simplify the expression inside the second fraction:

(12x + 26)

This expression can be factored out a common factor of 2:

2(6x + 13)

Now, we can substitute these simplified expressions back into the original polynomial expression:

[(x - 3)(x + 3)] / [(x - 2)(x + 2)] * (4(x - 2)) / (2(6x + 13))

Now, let's cancel out any common factors:

(x - 3)(x + 3) / (x - 2)(x + 2) * 2(x - 2) / (6x + 13)

Now, rearrange the expression:

[(x - 3)(x + 3) * 2(x - 2)] / [(x - 2)(x + 2)(6x + 13)]

Multiply the numerators and the denominators:

[2(x - 3)(x + 3)(x - 2)] / [(x - 2)(x + 2)(6x + 13)]

Finally, simplify if possible:

2(x - 3)(x + 3)(x - 2) / (x - 2)(x + 2)(6x + 13)

This is the polynomial expression in its simplest form.