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Perform the indicated operations and reduce to lowest terms. Assume that no denominator has a value of zero. ​

Perform The Indicated Operations And Reduce To Lowest Terms Assume That No Denominator Has A Value Of Zero class=

Sagot :

MrRoyalidn

Answer:

[tex]\frac{x}{9}[/tex]

Step-by-step explanation:

Given

[tex]\frac{x^2 - 9}{9x + 27} \div \frac{x - 3}{x}[/tex]

Required

Solve

[tex]\frac{x^2 - 9}{9x + 27} \div \frac{x - 3}{x}[/tex]

Change the division to multiplication

[tex]\frac{x^2 - 9}{9x + 27} * \frac{x}{x - 3}[/tex]

Apply difference of 2 squares

[tex]\frac{(x - 3)(x+3)}{9x + 27} * \frac{x}{x - 3}[/tex]

Cancel out x - 3

[tex]\frac{x+3}{9x + 27} * \frac{x}{1}[/tex]

Factorize 9x + 27

[tex]\frac{x+3}{9(x + 3)} * \frac{x}{1}[/tex]

Cancel out x + 3

[tex]\frac{1}{9} * \frac{x}{1}[/tex]

Finally, this gives:

[tex]\frac{x}{9}[/tex]

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