- #1

velox_xox

- 34

- 0

## Homework Statement

Simplify. (p

^{4}- q

^{4})/(p + q)

^{2}÷ 1/(p

^{2}+ q

^{2})

Answer: (p - q)/(p + q)

## Homework Equations

--

## The Attempt at a Solution

Transformed it to a multiplication problem.

(p

^{4}- q

^{4})/(p + q)

^{2}X (p

^{2}+ q

^{2})/1

Difference of the squares in the numerator of the first expression:

(p

^{2}+ q

^{2})(p

^{2}- q

^{2})/(p + q)

^{2}X (p

^{2}+ q

^{2})/1

Difference of the squares (once more) in the numerator of the first expression:

(p

^{2}+ q

^{2})(p + q)(p - q)/(p + q)

^{2}X (p

^{2}+ q

^{2})/1

Simplified the (p +q) from the numerator and denominator of the first equation:

(p

^{2}+ q

^{2})(p -q)/(p + q) X (p

^{2}+ q

^{2})/1

Simplified the (p

^{2}+ q

^{2}) from the numerators of both expressions:

(p - q)/(p + q)

My question is with the part. Is that proper form? A.k.a. Did I not bend the rules of algebra to get the correct answer? And if so, can someone give example of when simplifying both numerators is okay or not okay?

Thank you!

Last edited: