Question

Simplify the expression A/(βx + r) + B/(βx + r)^n.

a) A/(βx + r) + B/(βx + r)^n
b) A/βx + B/(βx + r)^n
c) A/(βx + r)^n + B/(βx + r)^n
d) A/(βx + r)^(n-1) + B/(βx + r)

Answer 1

To simplify the expression A/(βx + r) + B/(βx + r)^n, we need to find a common denominator and combine the fractions.

Step-by-step explanation:

To simplify the expression, A/(βx + r) + B/(βx + r)^n, we need to find a common denominator. The common denominator is (βx + r)^n. To do this, we can multiply the first fraction by (βx + r)^(n-1) and the second fraction by (βx + r)^(n-n), which is just 1. This gives us:

A/(βx + r) + B/(βx + r)^n = A(βx + r)^(n-1)/(βx + r)^(n-1)(βx + r) + B/(βx + r)^n

= A(βx + r)^(n-1)/(βx + r)^n + B/(βx + r)^n

Now that we have a common denominator, we can combine the fractions:

A(βx + r)^(n-1)/(βx + r)^n + B/(βx + r)^n = (A(βx + r)^(n-1) + B)/(βx + r)^n

So the simplified expression is (A(βx + r)^(n-1) + B)/(βx + r)^n.