Two Denominators

x/2 + x/3 = 10: half a number plus a third of it is 10. Two denominators, 2 and 3. Multiply everything by a number both divide into, their least common multiple, which is 6:

6 × x/2 + 6 × x/3 = 6 × 10

3x + 2x = 60

5x = 60

x = 12

Check: 12/2 + 12/3 = 6 + 4 = 10.

Any common multiple works (30 would do), but the least one keeps the numbers small. Another road: collect the two fractions of x directly, x/2 + x/3 = 5/6 x, and undo the coefficient. Both are legal; clearing denominators is the one that generalises to messier equations.