Computing Rational Functions

For the given functions f(x) and g(x), do the following computation. Choose the best answer.

f(x)=
5x+1

8x−1
and g(x)=
3x

8x−1

Find
f

g
(x)

Question

Computing Rational Functions

For the given functions f(x) and g(x), do the following computation. Choose the best answer.

f(x)=
5x+1

8x−1
 and g(x)=
3x

8x−1

Find 
f

g
(x)

BlackTom AI · Accepted Answer

We are given f(x) = (5x + 1)/(8x − 1) and g(x) = (3x)/(8x − 1), and asked to find (f/g)(x) = f(x) / g(x).

Start by writing the quotient of the two functions:
(f/g)(x) = [(5x + 1)/(8x − 1)] ÷ [(3x)/(8x − 1)].

Dividing by a fraction is equivalent to multiplying by its reciprocal, so we multiply by (8x − 1)/(3x):
(f/g)(x) = [(5x + 1)/(8x − 1)] × [(8x − 1)/(3x)].

Notice that the (8x − 1) factors cancel each other, as long as x ≠ 1/8 (the domain restriction from the original fractions):
(f/g)(x) = (5x + 1) / (3x).

Thus, the simplified expression for the quotient is (5x + 1)/(3x). If you were choosing from multiple options, the correct form would match this expression, while any option that fails to cancel the common (8x − 1) factor or that incorrectly handles the division by g(x) would be incorrect.

MAT-265-OD24-02-7799

Computing Rational Functions For the given functions f(x) and g(x), do the following computation. Choose the best answer. f(x)= 5x+1 8x−1 and g(x)= 3x 8x−1 Find f g (x)

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