I'm stuck on this question, any ideas? thanks

Step-by-step explanation:

So we have the limit:

Let's remove the fractions in the denominator by multiplying both layers by (6+x)(6). So:

Distribute:

Simplify the numerator:

Both the numerator and the denominator have an x. Cancel:

Direct substitution:

Simplify:

And that's our answer.

And we're done!

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Step-by-step explanation:

lim(x→0) [1/(6 + x) − 1/6] / x

The common denominator of the two fraction in the numerator is 6(6 + x) = 36 + 6x.

lim(x→0) [6/(36 + 6x) − (6 + x)/(36 + 6x)] / x

Combine the fractions.

lim(x→0) [(6 − 6 − x) / (36 + 6x)] / x

Simplify.

lim(x→0) [-x / (36 + 6x)] / x

Divide.

lim(x→0) -1 / (36 + 6x)

Evaluate.

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