SOLUTION: Solve and check for x: {{{4/(3x)}}} + {{{1/x}}} = {{{14/(3x^2)}}}

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Solve and check for x: {{{4/(3x)}}} + {{{1/x}}} = {{{14/(3x^2)}}}      Log On


   

Question 86294: Solve and check for x:
4%2F%283x%29 + 1%2Fx = 14%2F%283x%5E2%29
Answer by scianci(186) About Me  (Show Source):
You can put this solution on YOUR website!
4%2F%283x%29 + 1%2Fx = 14%2F%283x%5E2%29
Multiply everything by the LCD of the fractions, which is 3x%5E2:
3x%5E24%2F%283x%29 + 3x%5E21%2Fx = 3x%5E214%2F%283x%5E2%29
Let the denominators cancel out:
4x + 3x = 14
Solve in the usual manner:
7x = 14
%287x%29%2F7 = 14%2F7
x = 2 [potentially]
Must check for extraneous solutions/zero denominators:
3x = 3(2) which isn't = 0 so OK
3x%5E2 = 3(2)^2 = 12 which isn't = 0 so OK
x = 2 is a valid solution