Simplify the following. (1.) $$ \frac{ ext { I } 1-x^{2}+8 x}{4 x^{2}} $$ I (2. $$ \frac{x^{2}-12 x+27}{4 x^{2}-12 x} $$ (3) $$ \frac{6 x^{3}-2 x^{2}}{-3 x-9} imes \frac{x^{2}-9}{2-6 x} $$ (3-4

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Simplify the following. (1.) $$ \frac{	ext { I } 1-x^{2}+8 x}{4 x^{2}} $$ I (2. $$ \frac{x^{2}-12 x+27}{4 x^{2}-12 x} $$ (3) $$ \frac{6 x^{3}-2 x^{2}}{-3 x-9} 	imes \frac{x^{2}-9}{2-6 x} $$ (3-4

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Calculate or simplify the expression $$ (1-x^{2}+8x)/(4x^{2}) $$.
Divide the polynomials by following steps:
- step0: Using Long Division to Divide Polynomials:
  $$\frac{\left(1-x^{2}+8xight)}{\left(4x^{2}ight)}$$
- step1: Calculate:
  $$-\frac{1}{4}+\frac{8x+1}{4x^{2}}$$
Calculate or simplify the expression $$ (x^{2}-12x+27)/(4x^{2}-12x) $$.
Simplify the expression by following steps:
- step0: Solution:
  $$\frac{\left(x^{2}-12x+27ight)}{\left(4x^{2}-12xight)}$$
- step1: Remove the parentheses:
  $$\frac{x^{2}-12x+27}{4x^{2}-12x}$$
- step2: Factor the expression:
  $$\frac{\left(x-3ight)\left(x-9ight)}{4x\left(x-3ight)}$$
- step3: Reduce the fraction:
  $$\frac{x-9}{4x}$$
Calculate or simplify the expression $$ (6x^{3}-2x^{2})/(-3x-9) 	imes (x^{2}-9)/(2-6x) $$.
Simplify the expression by following steps:
- step0: Solution:
  $$\frac{\frac{\left(6x^{3}-2x^{2}ight)}{\left(-3x-9ight)}	imes \left(x^{2}-9ight)}{\left(2-6xight)}$$
- step1: Remove the parentheses:
  $$\frac{\frac{6x^{3}-2x^{2}}{-3x-9}	imes \left(x^{2}-9ight)}{2-6x}$$
- step2: Rewrite the fraction:
  $$\frac{-\frac{6x^{3}-2x^{2}}{3x+9}	imes \left(x^{2}-9ight)}{2-6x}$$
- step3: Multiply the terms:
  $$\frac{-\frac{\left(6x^{3}-2x^{2}ight)\left(x-3ight)}{3}}{2-6x}$$
- step4: Multiply by the reciprocal:
  $$-\frac{\left(6x^{3}-2x^{2}ight)\left(x-3ight)}{3}	imes \frac{1}{2-6x}$$
- step5: Rewrite the expression:
  $$-\frac{-x^{2}\left(-6x+2ight)\left(x-3ight)}{3}	imes \frac{1}{-6x+2}$$
- step6: Reduce the fraction:
  $$-\frac{-x^{2}\left(x-3ight)}{3}	imes 1$$
- step7: Multiply the terms:
  $$\frac{x^{2}\left(x-3ight)}{3}$$
- step8: Multiply the terms:
  $$\frac{x^{3}-3x^{2}}{3}$$
The simplified expressions are:
1. $$ \frac{1-x^{2}+8x}{4x^{2}} = -\frac{1}{4} + \frac{8x+1}{4x^{2}} $$
2. $$ \frac{x^{2}-12x+27}{4x^{2}-12x} = \frac{x-9}{4x} $$
3. $$ \frac{6x^{3}-2x^{2}}{-3x-9} 	imes \frac{x^{2}-9}{2-6x} = \frac{x^{3}-3x^{2}}{3} $$
Simplify the expressions as follows: 1. $$ \frac{1 - x^{2} + 8x}{4x^{2}} = -\frac{1}{4} + \frac{8x + 1}{4x^{2}} $$ 2. $$ \frac{x^{2} - 12x + 27}{4x^{2} - 12x} = \frac{x - 9}{4x} $$ 3. $$ \frac{6x^{3} - 2x^{2}}{-3x - 9} 	imes \frac{x^{2} - 9}{2 - 6x} = \frac{x^{3} - 3x^{2}}{3} $$

Simplify the following. (1.) \( \frac{\text { I } 1-x^{2}+8 x}{4 x^{2}} \) I (2. \( \frac{x^{2}-12 x+27}{4 x^{2}-12 x} \) (3) \( \frac{6 x^{3}-2 x^{2}}{-3 x-9} \times \frac{x^{2}-9}{2-6 x} \) (3-4

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