w/7 - 7/w = 0
By symmetry, w=7 or -7.
Alternatively,
w/7-7/w=0
w/7=7/w
w^2 = 49
w=±7
To solve the equation w/7 - 7/w = 0, we can follow these steps:
Step 1: Multiply both sides of the equation by the least common denominator (LCD) to eliminate the fractions. In this case, the LCD is 7w because it contains both denominators.
w/7 * 7w - 7/w * 7w = 0 * 7w
This simplifies to:
w^2 - 49 = 0
Step 2: Rearrange the equation so that one side is equal to zero.
w^2 - 49 = 0
Step 3: Factor the quadratic equation, if possible, or use the quadratic formula to solve for w.
In this case, the quadratic equation w^2 - 49 can be factored as the difference of squares:
(w - 7)(w + 7) = 0
Step 4: Set each factor equal to zero and solve for w.
Setting w - 7 = 0 gives:
w = 7
Setting w + 7 = 0 gives:
w = -7
Therefore, the solutions to the equation w/7 - 7/w = 0 are w = 7 and w = -7.