What is one possible solution to the rational equation `(1)/(x)-(2)/(x-2)=3`?

Answer

A, B, C

Explanation

Difficult: Medium
Category: Passport to Advanced Math/ Exponents
Strategic advice: Solving a rational equation is sometimes easier than just adding two rational expressions. You still may need to find a common denominator, but once you multiply both side of the equation by that denominator, you're left with much nicer looking equation to solve.
Getting to the Answer: Multiplying both sides of the equation by the common denominator `(x)(x-2)` yields the following:
`[(x(x-2))/(1)]*[(1)/(x)-(2)/(x-2)=3]`
`1(x-2)-2x=3(x)(x-2)`
`x-2-2x=3(x^(2)-2x)`
`-x-2=3x^(2)-6x`
`0=3x^(2)-5x+2`
Now, factor the equation for use the quadratic formula, set each factor equal to 0, solve for x and check that the solutions don't result in a zero denominator:
`0=3x^(2)-5x+2`
`0=(3x-2)(x-1)`
The solutions are `x=(2)/(3) and x=1`, both of which are valid solutions, so grib in ether values.