1+4/x=3/x-1 write down any restrictions and solve for x
The equation is:
1 + 4/x = 3/x - 1
To solve for x, first we need to get rid of the denominators. We can do that by multiplying both sides by x(x-1):
x(x-1) [1 + 4/x] = x(x-1) [3/x - 1]
Simplifying:
x(x-1) + 4(x-1) = 3(x(x-1))/x - x(x-1)
Expanding and collecting like terms:
x^2 - x + 4x - 4 = 3(x - 1) - x^2 + x
Simplifying:
x^2 - x + 4x - 4 = 3x - 3 - x^2 + x
Bringing the x^2 terms together and simplifying:
2x^2 - 2x + 4x - 3x + 4 - 3 = 0
2x^2 - x + 1 = 0
Finally, we can use the quadratic formula to solve for x:
x = [-(-1) ± sqrt((-1)^2 - 4(2)(1))]/(2*2)
x = [1 ± sqrt(1 - 8)]/4
x = [1 ± sqrt(-7)]/4
Since the square root of a negative number is not a real number, there are no solutions to this equation. Therefore, there are no restrictions on x.