Simplify the complex fraction

Question

 4x-16

_______

y

________

x^2  -16

________

y^2

Answer 1

this problem consists of one rational algebraic fraction being divided by another.

 

factor the first fraction; invert the second fraction, after factoring it, and place it alongside the first fraction, so that they could be multiplied.

 

now do as much cancellation of identical factors (one in numerator, other in denominator) and you will develop the answer.

Answer 2

The rule for division of fractions is "invert and multiply".  The complex fraction becomes a little easier:

(4(x-4) * y²)/(y(x-4)(x+4)

Note that I did a little factoring along the way.

As long as y≠0 and x≠4 this simplifies by cancellation (otherwise known as dividing out) to: 4y/(x+4).

 

Do you know why there are conditions on y and x?