Question

1. \\(\frac{10x^{3}+50x^{2}+40x}{10x^{2}}\\)\
2. \\(\frac{12n^{11}+48n^{9}+36n^{3}}{6n^{7}}\\)\
3. \\(\frac{20x^{9}+32x^{4}+28x^{?}}{4x^{5}}\\)\
4. \\(\frac{81n^{4}+3n^{3}+9n^{2}}{9n^{8}}\\)

Explanation:

Step1: Split the fraction into terms

$\frac{10x^3 + 50x^2 + 40x}{10x^2} = \frac{10x^3}{10x^2} + \frac{50x^2}{10x^2} + \frac{40x}{10x^2}$

Step2: Simplify each term

$= x + 5 + \frac{4}{x}$

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Step1: Split the fraction into terms

$\frac{12n^{11} + 48n^9 + 36n^3}{6n^7} = \frac{12n^{11}}{6n^7} + \frac{48n^9}{6n^7} + \frac{36n^3}{6n^7}$

Step2: Simplify each term

$= 2n^4 + 8n^2 + \frac{6}{n^4}$

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Step1: Split the fraction into terms

$\frac{20x^9 + 32x^4 + 28x}{4x^5} = \frac{20x^9}{4x^5} + \frac{32x^4}{4x^5} + \frac{28x}{4x^5}$

Step2: Simplify each term

$= 5x^4 + \frac{8}{x} + \frac{7}{x^4}$

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Step1: Split the fraction into terms

$\frac{81n^4 + 3n^3 + 9n^2}{9n^8} = \frac{81n^4}{9n^8} + \frac{3n^3}{9n^8} + \frac{9n^2}{9n^8}$

Step2: Simplify each term

$= \frac{9}{n^4} + \frac{1}{3n^5} + \frac{1}{n^6}$

Answer:

1. $x + 5 + \frac{4}{x}$
2. $2n^4 + 8n^2 + \frac{6}{n^4}$
3. $5x^4 + \frac{8}{x} + \frac{7}{x^4}$
4. $\frac{9}{n^4} + \frac{1}{3n^5} + \frac{1}{n^6}$