The concept of reducing complex fractions
"by multiplying the numerator and denominator ... by the common denominator of the denominators"
is absolutely correct. However, the example does not show much because the
only denominator that it uses is the 3 of 2/3.
Let us consider two different problems. First,
x
x
( 15 )
15x
=
=
2
x
–
3
5
(
2
x
)
–
3
5
(15)
10 – 3x
a problem where we reduce by multiplying the numerator and denominator by 15,
the common denominator for the two fractions 2/3 and x/5
The second problem is
x
7
x
7
( 105 )
15x
=
=
2
x
–
3
5
(
2
x
)
–
3
5
(105)
70 – 21x
Here we multiply by 105, the least common denominator for 3, 5, and 7.
