Rich G. answered • 02/15/19

Experienced Algebra Tutor at High School and College Level

The easier way to do a problem like this is by factoring instead of long division.

With ^{(48x + 32y)}/_{32 }, all the terms (48, 32, and 32 in the denominator) can be divided by 16. If we factor out a 16 from top and bottom we would get

^{16 (3x + 2y)}/_{16(2)}

Since 16/16 = 1, we can reduce the equation to ^{(3x + 2y)}/_{2}

We can now write the equation as addition of two fractions

^{3x}/_{2} + ^{2y}/_{2}

Since 2y/2 = y, we can write the answer as

^{3x}/_{2} + y_{ }