You are dealing with the concept of common denominators here. You need to get a common denominator for -1/2 and -4/3 seeing that these two terms will need to be added together to solve for this equation algebraically. The 1/5 is not an issue (do not need to find a common denominator) because it is a coefficient of the variable v, such that after getting 1/5v by itself on one side of the equation, both sides of the equation will be multiplied by 5 to get rid of 1/5 in the 1/5v term. there is no need to get a common denominator when multiplying or dividing, and anyways, it becomes a whole number, 5.
Step 1: Find the least common denominator (LCD) for -1/2 and -4/3. it is 6.
Step 2: Multiply the denominator, and hence the numerator (because we must do the same to both the top and bottom) by a number/number that results in the denominator being 6, which is the LCD in this problem.
-1/2 *(3/3) = -3/6
-4/3*(2/2) = -8/6
Step 3: We need to solve for v, so get everything that is not v, to other side of equation. Bring -4/3 (which is now -8/6) to left side of equation by adding it to both sides of the equation. adding -8/6 to -1/2 (which is now -3/6) gives
-3/6 + 8/6 = 5/6
Step 4 :We now have 5/6 = 1/5v. solve for v by multiplying both sides of equation by 5, to get rid of 1/5.
(5/6)*5 = 25/6
v = 25/6
Cannot reduce any further, so this is the final answer. Always plug back into original equation as a way to check that you got the correct answer.
Let me know if any questions.