simplify the expression with the restriction
5p/2q-p+10q/p-2q
Assuming the usual carelessness with parentheses,
5p/(2q-p) + 10q/(p-2q)
= (5p-10q)/(2q-p)
= 5(p-2q)/(2q-p)
= -5 if 2q≠p
To simplify the expression (5p/2q - p + 10q)/(p - 2q) with the given restriction, let's break it down into steps:
Step 1: Simplify the numerator
Combine the terms in the numerator (5p/2q - p + 10q) by finding a common denominator. The common denominator is 2q, so we adjust the terms accordingly:
(5p - 2pq + 20q)/(2q)
Step 2: Factor out a common term
In the numerator, we notice that all three terms share a common factor of p. Let's factor out p:
p(5 - 2q + 20q)/(2q)
Step 3: Combine like terms in the numerator
Simplify the expression inside the parentheses:
(5p + 18pq)/(2q)
Step 4: Apply the restriction
Now, we need to apply the given restriction, which is (p - 2q) in the denominator. We can't have p = 2q since it would result in dividing by zero. Thus, we need to exclude this value from our solution.
Final Answer:
(5p + 18pq)/(2q) with the restriction p ≠ 2q.