solve: 3/v = 6/v - 1/5
multiply each term by 5v
15 = 30 - v
v = 15
To solve the equation 3/v = 6/v - 1/5, we need to simplify both sides and isolate the variable v.
First, let's find a common denominator for the fractions on the right-hand side. The least common multiple (LCM) of v and 5 is 5v.
Multiplying 6/v by 5/5, we get (6 * 5) / (v * 5) = 30/5v.
The equation now becomes 3/v = 30/5v - 1/5.
Next, let's combine the fractions on the right-hand side by finding a common denominator, which is 5v.
30/5v - 1/5 = (30 - v) / (5v).
Now we have the equation 3/v = (30 - v) / (5v).
To eliminate the fractions, we can cross multiply. This means multiplying the numerator of the left side by the denominator of the right side and multiplying the denominator of the left side by the numerator of the right side.
Cross multiplying gives us: 3 * (5v) = v * (30 - v).
Simplifying further, we have: 15v = 30v - v^2.
Rearranging the terms, we get: v^2 - 15v + 30v = 0.
Combining like terms, we have: v^2 + 15v = 0.
Factoring out the common factor v, we have: v(v + 15) = 0.
Setting each factor equal to zero, we have two possible solutions: v = 0 and v + 15 = 0. Solving for v in each case:
For v = 0, we have the solution v = 0.
For v + 15 = 0, we subtract 15 from both sides to get v = -15.
Therefore, the solutions to the equation 3/v = 6/v - 1/5 are v = 0 and v = -15.