Question

P+2q/ 3p-q - 5q-2p/q-3p

Answer 1

(P+2q)/ (3p-q) - (5q-2p)/(q-3p) =(P+2q)/ (3p-q) + (5q-2p)/(3p-q) = 
= (P+2q +5q-2p)/(3p-q) = (7q-p)/(3p-q)

Answer 2

To simplify the expression, let's combine like terms and find a common denominator. The given expression is:

$\frac{p+2q}{3p-q} - \frac{5q-2p}{q-3p}$

Step 1: Find a common denominator for both fractions. The common denominator is $(3p-q)(q-3p)$.

Step 2: Convert both fractions to have the common denominator:

$\frac{p+2q}{3p-q} \cdot \frac{(q-3p)}{(q-3p)} - \frac{5q-2p}{q-3p} \cdot \frac{(3p-q)}{(3p-q)}$

Step 3: Simplify the numerators:

$\frac{(p+2q)(q-3p)}{(3p-q)(q-3p)} - \frac{(5q-2p)(3p-q)}{(q-3p)(3p-q)}$

Step 4: Combine the fractions:

$\frac{(p+2q)(q-3p) - (5q-2p)(3p-q)}{(3p-q)(q-3p)}$

Step 5: Expand the terms:

$\frac{pq - 3p^2 + 2q^2 - 6q - (15pq - 7p^2 - 5q^2 + 6pq)}{(3p-q)(q-3p)}$

Step 6: Combine like terms in the numerator:

$\frac{-2p^2 + 2q^2 - 6q - (-8pq - 5q^2)}{(3p-q)(q-3p)}$

Step 7: Simplify further:

$\frac{-2p^2 + 2q^2 - 6q + 8pq + 5q^2}{(3p-q)(q-3p)}$

Step 8: Combine like terms in the numerator:

$\frac{8pq - 2p^2 + 7q^2 - 6q}{(3p-q)(q-3p)}$

So the simplified expression is:

$\frac{8pq - 2p^2 + 7q^2 - 6q}{(3p-q)(q-3p)}$