Question

The denominator of a fraction is one more than thrice the numerator.the difference between the reciprocal of the fraction is 15/4.find the fraction

Answer 1

Step-by-step explanation:

put the words into math ...

fraction = n/(3n+1)

so now do the math

(3n+1)/n - n/(3n+1) = 15/4

now just find n and thus the fraction

Answer 2

Answer:

FRACTION IS 1/4.

Step-by-step explanation:

• In context to the given question, we have to find the fraction for the given situation.
• GIVEN:

Let the number be 'n'

Fraction = n/(3n+1)

Difference of reciprocal of fraction = ($\frac{n}{3n+1}$) - ($\frac{3n+1}{n}$) = $\frac{15}{4}$

• SOLUTION:

Difference of reciprocal = $\frac{n}{3n+1}$  -  $\frac{3n+1}{n}$ = $\frac{15}{4}$

LCM = (3n+1)(n)

Difference of reciprocal =  $\frac{n² - (3n+1)²}{(3n+1)(n)}$ = $\frac{15}{4}$

= [n²-(9n²+6n+1)]/3n²+n = 15/4

by transposing method, we get

⇒ -8n²-6n-1 = [45n²+15n]  /4    

⇒  4(-8n²-6n-1) = [45n²+15n]

⇒ -32n²-24n-4 = 45n²+15n

⇒ 45n²+15n -32n²-24n-4 =0

⇒ 13n²-9n-4 = 0

⇒ by finding roots , we get

⇒  13n²-13n+ 4n-4

⇒ 13n(n-1) + 4(n-1) =0

therefore, two roots are

13n+4 = 0                                n-1=0

n = -4/13                                  n=1

For both the values, n =1 SATISFY THE GIVEN CONDITION

THERFORE, FRACTION IS 1/4