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

Solution:

1 over 36 minus 1 over x squared all over 1 over 6 plus 1 over x

It can be mathematically represented as

[ (1 / 36) - (1 / x²) ] / [ (1 / 6) + (1 / x) ]

Taking LCM

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

We know that

x² - 36 = (x + 6)(x - 6)

So we get

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

Here

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

= [ (x+6)(x-6) / 6x ] × [ 1 / (x+6) ]

= (x - 6) / 6x

Therefore, quantity 1 over 36 minus 1 over x squared all over 1 over 6 plus 1 over x is (x - 6) / 6x.

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

Summary:

Simplifying quantity 1 over 36 minus 1 over x squared all over 1 over 6 plus 1 over x, we get (x - 6) / 6x.