Question

Can someone plz explain this to me i would appreciate the help!

Answer 1

Answer:
`(6)/(65)`

Explanation:

`((1)/(2)-(2)/(5) )/((1)/(3)+(3)/(4))`

Let's solve each separately.

`(1)/(2)-(2)/(5)=((1)(5)-(2)(2))/((2)(5)) =(5-4)/(10) =(1)/(10)`

`(1)/(3)+(3)/(4)=((1)(4)+(3)(3))/((3)(4)) =(4+9)/(12) =(13)/(12)`

This leaves the fraction as;

`((1)/(10) )/((13)/(12) )`

To get rid of the fraction in the denominator, multiply by its reciprocal. The reciprocal of a fraction is the same fraction but inverted.

`((1)/(10) )/((13)/(12) )*(12)/(13)`

This will eliminate the denominator, leaving the fraction like;

`(1)/(10)*(12)/(13)`

12 and 10 can be simplified.

12/2=6

10/2=5

Our new fraction would be;

`(1)/(5)*(6)/(13)`

Multiply;

`(6)/(65)`