Question

Simplify the expression (pq/p²-q² q/q-p)/(p-q (4qq²-p²/p q))

Answer 1

To simplify the expression, do the following steps: Simplify the denominator, cancel out the q terms, simplify the denominator further, and multiply both numerator and denominator by p.

Step-by-step explanation:

To simplify the expression, let's break it down step by step:

Step 1: Simplify the denominator of the fraction on the left side of the expression:

(pq/p²-q²) = p+q (since (p²-q²) = (p+q)(p-q))

So, the expression becomes:

(p+q)(q/q-p)/(p-q (4qq²-p²/p q))

Step 2: Cancel out the q terms in the numerator and denominator:

=(p+q)/(-1)(p-q (4qq²-p²/p q))

Step 3: Simplify the denominator:

= -(p+q)/(p-q(4q-p)/p)

Step 4: Multiply both numerator and denominator by p to remove the fraction in the denominator:

= -p(p+q)/(p-q(4q-p))

Therefore, the simplified expression is -p(p+q)/(p-q(4q-p)).