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Georgia [21]
3 years ago
15

Simplify quantity 1 over 36 minus 1 over x squared all over 1 over 6 plus 1 over x.

Mathematics
1 answer:
Ne4ueva [31]3 years ago
7 0
 <span>[ (1 / 36) - (1 / x²) ] / [ (1 / 6) + (1 / x) ] 

[ (x² - 36) / 36x² ] / [ (x + 6) / 6x ] 

</span>remember that<span>: 
x² - 36 = (x + 6)(x - 6) 

so

[ (x+6)(x-6) / 36x² ] / [ (x + 6) / 6x ] 


[ (x+6)(x-6) / 36x² ] * [ 6x / (x + 6) ] 


6x / 36x² = 1 / 6x 


[ (x+6)(x-6) / 6x ] * [ 1 / (x+6) ] -------------------- > </span>(x - 6) / 6x<span>

The answer is </span>(x - 6) / 6x<span>

</span>
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Step-by-step explanation:

Factor

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Divide by 3 and factor

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"Theory:

A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =

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Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression."

I put a picture to help u understand.

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