Question

Simplify. 1/4n-1/2 / n/6 - 1/24n A. -6 / 2N-1 B. -6 / 2N+1 C. 6 / 2N+1

Answer 1

Answer:

Option B. is the right answer.

Step-by-step explanation:

We have to simplify the given fraction $\frac{\frac{1}{4n}-\frac{1}{2}}{\frac{n}{6}-\frac{1}{24n}}$

Now we will solve numerator first

${\frac{1}{4n}-\frac{1}{2}}$ $=\frac{(1-2n)}{4n}$

Then we will solve denominator

$=\frac{n}{6}-\frac{1}{24n}$$=\frac{4n^{2}-1}{24n}$

$=-\frac{-4n^{2}+1}{24n}$$=-\frac{(1-2n)(1+2n)}{24n}$

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

$-\frac{(1-2n)}{4n}\div \frac{(1-2n)(1+2n)}{24n}$

$=-\frac{(1-2n)}{4n}\times \frac{24n}{(1-2n)(1+2n)}$

$=-\frac{6}{2n+1}$

Therefore option B is the right answer.

Answer 2

Answer:

Option B is the correct answer

Step-by-step explanation:

The exact expression is:

$\frac{\frac{1}{4n}-\frac{1}{2}}{\frac{n}{6}-\frac{1}{24n} }$

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

$\frac{\frac{1-2n}{4n} }{\frac{4n^{2}-1 }{24n}} \\\\=\frac{1-2n}{4n}\times\frac{24n}{4n^{2}-1 }\\\\=\frac{1-2n}{4n}\times\frac{24n}{(2n+1)(2n-1)}\\\\ =-\frac{2n-1}{4n}\times\frac{24n}{(2n+1)(2n-1)}\\\\ =-\frac{6}{2n+1}$