x/3-2/3=1/x
*Solve the rational below.
I really need help.
Multiply through by 3x
x^2 -2x = 3
And solve.
I don't get it...
can you explain it more.then I can help you Margie
Certainly, I'll explain it step-by-step for you, Margie.
The given rational equation is: x/3 - 2/3 = 1/x
Step 1: To get rid of the fractions in the equation, we can multiply every term in the equation by the least common denominator (LCD) of the fractions involved. In this case, the LCD is 3x.
So, we multiply both sides of the equation by 3x:
(3x) * (x/3) - (3x) * (2/3) = (3x) * (1/x)
This simplifies to:
(x^2)/1 - (2x)/1 = 3
Step 2: We combine like terms on the left side of the equation:
(x^2 - 2x) = 3
So now, our equation becomes:
x^2 - 2x = 3
Step 3: We bring all terms to one side of the equation by subtracting 3 from both sides:
x^2 - 2x - 3 = 0
Step 4: Now that we have a quadratic equation in the standard form ax^2 + bx + c = 0, we can factor or use the quadratic formula to solve for x.
In this case, the equation can be factored as:
(x - 3)(x + 1) = 0
Step 5: Set each factor equal to zero and solve for x:
x - 3 = 0 or x + 1 = 0
This gives us two possible solutions:
x = 3 or x = -1
So, the solutions to the rational equation are x = 3 and x = -1.
I hope this explanation helps clarify the steps involved in solving the given rational equation. Let me know if there's anything else I can assist you with!