Question

Write the simplest form and identify the non-permissible values.

Answer 1

$\frac{4(x^{2} - 9)^{2} - (x + 3)^{2}}{x^{2}] =\frac{4((x^{2} - 9)(x^{2} - 9)) - ((x + 3)(x + 3))}{x^{2} + 6x + 9}$ + 6x + 9} =\frac{4(x^{4} - 9x^{2} - 9x^{2} + 81) - (x^{2} + 3x + 3x + 9)}{x^{2} + 6x + 9} =\frac{4(x^{4} - 18x^{2} + 81) - (x^{2} + 6x + 9)}{x^{2} + 6x + 9} = \frac{4x^{4} - 72x^{2} + 324 - (x^{2} + 6x + 9)}{x^{2} + 6x + 9} =\frac{4x^{4} - 72x^{2} - x^{2} + 6x + 324 + 9}{x^{2} + 6x + 9} =\frac{4x^{4} - 73x^{2} + 6x + 333}{x^{2} + 6x + 9} = 4x^{2} - 24x + 35 + \frac{12x + 18}{x^{2} + 6x + 9}[/tex]