Question

Simplify. 1/4n-1/2 / n/6 - 1/24n

A. -6 / 2N-1
B. -6 / 2N+1
C. 6 / 2N+1

Answer 1

Option B. is the right answer.

Explanation:

We have to simplify the given fraction
`((1)/(4n)-(1)/(2))/((n)/(6)-(1)/(24n))`

Now we will solve numerator first

`{(1)/(4n)-(1)/(2)}`
`=((1-2n))/(4n)`

Then we will solve denominator

`=(n)/(6)-(1)/(24n)`
`=(4n^(2)-1)/(24n)`

`=-(-4n^(2)+1)/(24n)`
`=-((1-2n)(1+2n))/(24n)`

Now we put numerator and denominator in the form of a fraction.

`-((1-2n))/(4n)/ ((1-2n)(1+2n))/(24n)`

`=-((1-2n))/(4n)* (24n)/((1-2n)(1+2n))`

`=-(6)/(2n+1)`

Therefore option B is the right answer.

Answer 2

Option B is the correct answer

Explanation:

The exact expression is:

`((1)/(4n)-(1)/(2))/((n)/(6)-(1)/(24n) )`

Taking LCM in numerator and denominator can simplify the expression. Further simplifying the expression can give us the final result, as shown below:

`((1-2n)/(4n) )/((4n^(2)-1 )/(24n)) \\\\=(1-2n)/(4n)*(24n)/(4n^(2)-1 )\\\\=(1-2n)/(4n)*(24n)/((2n+1)(2n-1))\\\\ =-(2n-1)/(4n)*(24n)/((2n+1)(2n-1))\\\\ =-(6)/(2n+1)`