x/3-2/3=1/x
*Solve the rational below.
I really need help.
multiply both sides by x.
x^2/3 -2x/3 = 1
multiply both sides by 3
subtract three from each side
x^2 -2x -3=0
(x-3)(x+1)=0
Then either of the factors can be zero, or x=3 or x=-1
To solve the given rational equation, follow these steps:
Step 1: Multiply both sides of the equation by the common denominator, which in this case is 3x, to eliminate the denominator:
3x * (x/3) - 3x * (2/3) = 3x * (1/x)
This simplifies to:
x^2/3 - 2x/3 = 3
Step 2: Multiply both sides of the equation by 3 to get rid of the fractions:
3 * (x^2/3) - 3 * (2x/3) = 3 * 3
This simplifies to:
x^2 - 2x = 9
Step 3: Rearrange the equation to one side to set it equal to zero:
x^2 - 2x - 9 = 0
Step 4: Factor the quadratic trinomial:
(x - 3)(x + 3) = 0
Step 5: Set each factor equal to zero and solve for x:
x - 3 = 0 or x + 3 = 0
This gives the two possible solutions:
x = 3 or x = -3
Therefore, the solution to the rational equation is x = 3 or x = -3.