SOLUTION: How do you solve for x when it is in the denominator on both sides of a rational equation? And what are the restrictions for X? This is the problem: 4/x = 5/x - 1/2

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: How do you solve for x when it is in the denominator on both sides of a rational equation? And what are the restrictions for X? This is the problem: 4/x = 5/x - 1/2      Log On


   



Question 81644This question is from textbook Algebra I
: How do you solve for x when it is in the denominator on both sides of a rational equation? And what are the restrictions for X? This is the problem:
4/x = 5/x - 1/2
This question is from textbook Algebra I

Answer by tutorcecilia(2152) About Me  (Show Source):
You can put this solution on YOUR website!
The restrictions in this case is that x cannot equal to zero because you cannot divide by zero.
%284%2Fx%29 = %285%2Fx+-+1%2F2%29
%28%282x%294%2Fx%29 = %28%282x%295%2Fx+-+%282x%291%2F2%29 [find the LCD (2x); multiply each term by the LCD]
.
8=10-x [cancel wherever possible]
8=10-x [solve for the x-term]
8-8=10-8-x
0=2-x
-2=2-2-x
-2=-x
-2/-1=-x/-1
2=x
.
check by plugging (x=2) back into the original equation and solve:
%284%2Fx%29 = %285%2Fx+-+1%2F2%29
%284%2F2%29 = %285%2F2+-+1%2F2%29
2=%284%2F2%29
2=2 [checks out]