SOLUTION: Solve the equations and check your solutions. If there is no solutions, say so... 1/x+2/3x=1/3 5/4x+2=1/x

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Solve the equations and check your solutions. If there is no solutions, say so... 1/x+2/3x=1/3 5/4x+2=1/x      Log On


   

Question 315337: Solve the equations and check your solutions. If there is no solutions, say so...
1/x+2/3x=1/3
5/4x+2=1/x
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

1%2Fx%2B2%2F%283x%29=1%2F3

Put parentheses around every term:

%281%2Fx%29%2B%282%2F%283x%29%29=%281%2F3%29

Multiply every term through by LCD=red%28%283%2Ax%29%2F1%29



Do some cancelling:



All that's left is

3%2B2=x

5=x

Checking:

%281%2Fx%29%2B%282%2F%283x%29%29=%281%2F3%29
%281%2F5%29%2B%282%2F%283%2A5%29%29=%281%2F3%29
1%2F5%2B2%2F15=1%2F3
3%2F15%2B2%2F15=1%2F3
5%2F15=1%2F3
1%2F3=1%2F3

----------------------------

5%2F%284x%29%2B2=1%2Fx%29

Put parentheses around every term and write the 2 as 2%2F1:

%285%2F%284x%29%29%2B%282%2F1%29=%281%2Fx%29

Multiply every term through by LCD=red%28%284%2Ax%29%2F1%29



Do some cancelling:



All that's left is

5%2B8x=4

8x=-1

x=%28-1%29%2F8

x=-1%2F8

Edwin