Final answer:
To solve the equation x:2/x + 1/3 = 5/2, find a common denominator, add numerators, simplify fractions, and isolate x.
Step-by-step explanation:
To solve the fractional equation x:2/x + 1/3 = 5/2, we need to first find a common denominator for the two fractions on the left side of the equation. The common denominator for 2 and 3 is 6. We can rewrite the equation as 3x/6 + 2/6 = 5/2. Next, we can add the numerators together to get (3x + 2)/6 = 5/2. To eliminate the fraction, we can multiply both sides of the equation by 6 to get rid of the denominators. This gives us 3x + 2 = 15/2.
Next, we can simplify the fraction on the right side of the equation. Multiplying both the numerator and denominator by 2 gives us 15/2 = 30/4. Now we can rewrite the equation as 3x + 2 = 30/4. To solve for x, we can subtract 2 from both sides of the equation, which gives us 3x = 30/4 - 8/4 = 22/4. Finally, we can divide both sides of the equation by 3 to isolate x, giving us the solution x = 22/12 = 11/6.