Question

Consider the rational equation 1/R=(1/x)+(1/y).Find the value of R when x=2/5 and y=3/4.

Answer 1

R =
`(6)/(23)`

Explanation:

Given the rational equation as:

`(1)/(R)=(1)/(x)+(1)/(y)`

To find:

The value of R when x =
`\frac{\textup{2}}{\textup{5}}`

and, y =
`\frac{\textup{3}}{\textup{4}}`

now,

substituting the given values of x and y in the given rational equation,

`(1)/(R)=(1)/((2)/(5))+(1)/((3)/(4))`

or

⇒
`(1)/(R)=(5)/(2)+(4)/(3)`

or

⇒
`(1)/(R)=(5*3+4*2)/(2*3)`

or

⇒
`(1)/(R)=(15+8)/(6)`

or

⇒
`(1)/(R)=(23)/(6)`

now on rearranging, we get

⇒ R =
`(6)/(23)`