Solve each rational equation. State the restrictions.
𝑥−3/3𝑥− 1/4=1/2𝑥
To solve this rational equation, we will first find a common denominator for the fractions. The common denominator is 12 because it is the least common multiple of 3 and 4.
Now, we'll rewrite the equation with the common denominator:
(12𝑥-36) / (12𝑥) - (3) / (12) = (6𝑥) / (12)
Simplify the equation:
(12𝑥-36 - 3) / (12) = (6𝑥) / (12)
(12𝑥-39) / (12) = (6𝑥) / (12)
Since the denominators are the same, we can cancel them out:
12𝑥-39 = 6𝑥
Now, let's solve for 𝑥:
12𝑥-6𝑥 = 39
6𝑥 = 39
𝑥 = 39/6
Simplifying:
𝑥 = 6.5
Thus, the solution to the equation is 𝑥 = 6.5.
Restrictions: There are no restrictions in this equation.