$$ 4 x^{-5}-x^{-3}-7 x^{-4}+9 x^{-2}-7 x^{-1}+2 $$ entre $$ 4 x^{-2}+x^{-1}-3+2 x $$

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Simplify the expression by following steps:
- step0: Calculate:
  $$4x^{-2}+x^{-1}-3+2x$$
- step1: Simplify:
  $$\frac{4}{x^{2}}+x^{-1}-3+2x$$
- step2: Simplify:
  $$\frac{4}{x^{2}}+\frac{1}{x}-3+2x$$
- step3: Reduce fractions to a common denominator:
  $$\frac{4}{x^{2}}+\frac{x}{x\times x}-\frac{3x\times x}{x\times x}+\frac{2x\times x\times x}{x\times x}$$
- step4: Multiply the terms:
  $$\frac{4}{x^{2}}+\frac{x}{x^{2}}-\frac{3x\times x}{x\times x}+\frac{2x\times x\times x}{x\times x}$$
- step5: Multiply the terms:
  $$\frac{4}{x^{2}}+\frac{x}{x^{2}}-\frac{3x\times x}{x^{2}}+\frac{2x\times x\times x}{x\times x}$$
- step6: Multiply the terms:
  $$\frac{4}{x^{2}}+\frac{x}{x^{2}}-\frac{3x\times x}{x^{2}}+\frac{2x\times x\times x}{x^{2}}$$
- step7: Transform the expression:
  $$\frac{4+x-3x\times x+2x\times x\times x}{x^{2}}$$
- step8: Multiply the terms:
  $$\frac{4+x-3x^{2}+2x\times x\times x}{x^{2}}$$
- step9: Multiply the terms:
  $$\frac{4+x-3x^{2}+2x^{3}}{x^{2}}$$
Expand the expression $$ 4 x^{-5}-x^{-3}-7 x^{-4}+9 x^{-2}-7 x^{-1}+2 $$
Simplify the expression by following steps:
- step0: Calculate:
  $$4x^{-5}-x^{-3}-7x^{-4}+9x^{-2}-7x^{-1}+2$$
- step1: Simplify:
  $$\frac{4}{x^{5}}-x^{-3}-7x^{-4}+9x^{-2}-7x^{-1}+2$$
- step2: Simplify:
  $$\frac{4}{x^{5}}-\frac{1}{x^{3}}-7x^{-4}+9x^{-2}-7x^{-1}+2$$
- step3: Simplify:
  $$\frac{4}{x^{5}}-\frac{1}{x^{3}}-\frac{7}{x^{4}}+9x^{-2}-7x^{-1}+2$$
- step4: Simplify:
  $$\frac{4}{x^{5}}-\frac{1}{x^{3}}-\frac{7}{x^{4}}+\frac{9}{x^{2}}-7x^{-1}+2$$
- step5: Simplify:
  $$\frac{4}{x^{5}}-\frac{1}{x^{3}}-\frac{7}{x^{4}}+\frac{9}{x^{2}}-\frac{7}{x}+2$$
- step6: Reduce fractions to a common denominator:
  $$\frac{4}{x^{5}}-\frac{x^{2}}{x^{3}\times x^{2}}-\frac{7x}{x^{4}\times x}+\frac{9x^{2}\times x}{x^{2}\times x^{2}\times x}-\frac{7x\times x^{2}\times x}{x\times x\times x^{2}\times x}+\frac{2x\times x\times x^{2}\times x}{x\times x\times x^{2}\times x}$$
- step7: Multiply:
  $$\frac{4}{x^{5}}-\frac{x^{2}}{x^{5}}-\frac{7x}{x^{4}\times x}+\frac{9x^{2}\times x}{x^{2}\times x^{2}\times x}-\frac{7x\times x^{2}\times x}{x\times x\times x^{2}\times x}+\frac{2x\times x\times x^{2}\times x}{x\times x\times x^{2}\times x}$$
- step8: Multiply:
  $$\frac{4}{x^{5}}-\frac{x^{2}}{x^{5}}-\frac{7x}{x^{5}}+\frac{9x^{2}\times x}{x^{2}\times x^{2}\times x}-\frac{7x\times x^{2}\times x}{x\times x\times x^{2}\times x}+\frac{2x\times x\times x^{2}\times x}{x\times x\times x^{2}\times x}$$
- step9: Multiply:
  $$\frac{4}{x^{5}}-\frac{x^{2}}{x^{5}}-\frac{7x}{x^{5}}+\frac{9x^{2}\times x}{x^{5}}-\frac{7x\times x^{2}\times x}{x\times x\times x^{2}\times x}+\frac{2x\times x\times x^{2}\times x}{x\times x\times x^{2}\times x}$$
- step10: Multiply:
  $$\frac{4}{x^{5}}-\frac{x^{2}}{x^{5}}-\frac{7x}{x^{5}}+\frac{9x^{2}\times x}{x^{5}}-\frac{7x\times x^{2}\times x}{x^{5}}+\frac{2x\times x\times x^{2}\times x}{x\times x\times x^{2}\times x}$$
- step11: Multiply:
  $$\frac{4}{x^{5}}-\frac{x^{2}}{x^{5}}-\frac{7x}{x^{5}}+\frac{9x^{2}\times x}{x^{5}}-\frac{7x\times x^{2}\times x}{x^{5}}+\frac{2x\times x\times x^{2}\times x}{x^{5}}$$
- step12: Transform the expression:
  $$\frac{4-x^{2}-7x+9x^{2}\times x-7x\times x^{2}\times x+2x\times x\times x^{2}\times x}{x^{5}}$$
- step13: Multiply the terms:
  $$\frac{4-x^{2}-7x+9x^{3}-7x\times x^{2}\times x+2x\times x\times x^{2}\times x}{x^{5}}$$
- step14: Multiply the terms:
  $$\frac{4-x^{2}-7x+9x^{3}-7x^{4}+2x\times x\times x^{2}\times x}{x^{5}}$$
- step15: Multiply the terms:
  $$\frac{4-x^{2}-7x+9x^{3}-7x^{4}+2x^{5}}{x^{5}}$$
Calculate or simplify the expression $$ \frac{4+x-3x^{2}+2x^{3}}{x^{2}} $$.
Divide the polynomials by following steps:
- step0: Using Long Division to Divide Polynomials:
  $$\frac{4+x-3x^{2}+2x^{3}}{x^{2}}$$
- step1: Calculate:
  $$2x-3+\frac{x+4}{x^{2}}$$
Calculate or simplify the expression $$ \frac{4-x^{2}-7x+9x^{3}-7x^{4}+2x^{5}}{x^{5}} $$.
Divide the polynomials by following steps:
- step0: Using Long Division to Divide Polynomials:
  $$\frac{4-x^{2}-7x+9x^{3}-7x^{4}+2x^{5}}{x^{5}}$$
- step1: Calculate:
  $$2+\frac{-7x^{4}+9x^{3}-x^{2}-7x+4}{x^{5}}$$
Para resolver la expresión $$ \frac{4 x^{-5}-x^{-3}-7 x^{-4}+9 x^{-2}-7 x^{-1}+2}{4 x^{-2}+x^{-1}-3+2 x} $$, primero simplificamos tanto el numerador como el denominador.

### Paso 1: Simplificación del numerador

El numerador es:
$$
4 x^{-5}-x^{-3}-7 x^{-4}+9 x^{-2}-7 x^{-1}+2
$$
Al expandirlo, obtenemos:
$$
\frac{4 - x^{2} - 7x + 9x^{3} - 7x^{4} + 2x^{5}}{x^{5}}
$$
Simplificando, se convierte en:
$$
2 + \frac{-7x^{4} + 9x^{3} - x^{2} - 7x + 4}{x^{5}}
$$

### Paso 2: Simplificación del denominador

El denominador es:
$$
4 x^{-2}+x^{-1}-3+2 x
$$
Al expandirlo, obtenemos:
$$
\frac{4 + x - 3x^{2} + 2x^{3}}{x^{2}}
$$
Simplificando, se convierte en:
$$
2x - 3 + \frac{x + 4}{x^{2}}
$$

### Paso 3: División de las expresiones simplificadas

Ahora, tenemos:
$$
\frac{2 + \frac{-7x^{4} + 9x^{3} - x^{2} - 7x + 4}{x^{5}}}{2x - 3 + \frac{x + 4}{x^{2}}}
$$

Para simplificar esta expresión, podemos multiplicar el numerador y el denominador por $$ x^{5} $$ para eliminar las fracciones. Esto nos dará una expresión más manejable.

### Resultado final

La expresión simplificada es:
$$
\frac{(2x^{5} + (-7x^{4} + 9x^{3} - x^{2} - 7x + 4))}{(2x^{6} - 3x^{5} + (x + 4)x^{3})}
$$

Si necesitas más simplificaciones o un resultado numérico específico, házmelo saber.
Para simplificar la expresión $$ \frac{4 x^{-5}-x^{-3}-7 x^{-4}+9 x^{-2}-7 x^{-1}+2}{4 x^{-2}+x^{-1}-3+2 x} $$, primero expandimos y simplificamos tanto el numerador como el denominador. Luego, dividimos las dos expresiones simplificadas para obtener la forma final de la fracción.

\( 4 x^{-5}-x^{-3}-7 x^{-4}+9 x^{-2}-7 x^{-1}+2 \) entre \( 4 x^{-2}+x^{-1}-3+2 x \)

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