If `(7)/(m-sqrt(3))=(sqrt(3))/(m)+(4)/(2m)`, what is the value of m ?

Options

A. `-3.464`
B. `-1.978`
C. `-0.918`
D. `1.978`

Answer

B

Explanation

Before you can cross multiply, you need to express the right side of the equation as a single fraction. That means giving the two fractions a common denominator and adding them. The common denominator is 2m.
`(7)/(m-sqrt(3))=(sqrt(3))/(m)+(4)/(2m)`
`(7)/(m-sqrt(3))=(2sqrt(3))/(2m)+(4)/(2m)`
`(7)/(m-sqrt(3))=(2sqrt(3)+4)/(2m)`
Now you can cross multiply :
`(7)/(m-sqrt(3))=(2sqrt(3)+4)/(2m)`
`(7)(2m)=(m-sqrt(3))(2sqrt(3)+4)`
`14m=2sqrt(3)m-6+4m-4sqrt(3)`
`10-2sqrt(3)m=-6-4sqrt(3)`
`(10-2sqrt(3))m=-6-4sqrt(3)`
`m=(-6-4sqrt(3))/(10-2sqrt(3))~~-1.978`
This problem could also be solved by backsolving, explained on the next page. Just try the different choices for m, and when one of them works, you have the answer. Very often the more complicated equations, such as the one in this problem, can be solved more easily and quickly by backsolving.