Computing Rational Functions

For the given functions and , do the following computation. Choose the best answer.

and

Find

Question

Computing Rational Functions

For the given functions  and , do the following computation. Choose the best answer.

and

Find

BlackTom AI · Accepted Answer

To start, note the problem involves dividing two rational expressions. We are given f(x) = (5x + 1)/(8x − 1) and g(x) = (3x)/(8x − 1). The task is to compute (f/g)(x) = f(x) / g(x).

First, set up the division of fractions: f(x)/g(x) = [(5x + 1)/(8x − 1)] ÷ [3x/(8x − 1)]. This is equivalent to multiplying by the reciprocal: [(5x + 1)/(8x − 1)] × [(8x − 1)/(3x)].

Next, observe a common factor cancellation: the (8x − 1) factor appears in both the numerator and denominator across the two fractions, so they cancel when multiplied. This simplifies the expression to (5x + 1)/(3x).

Now, consider the domain considerations briefly: as long as x ≠ 0 and 8x − 1 ≠ 0 (i.e., x ≠ 1/8), the simplification is valid. The stepwise cancellation is permissible because we are multiplying by the reciprocal and the original denominators are nonzero.

Looking at possible final forms one could write for the result, the expression (5x + 1)/(3x) is the simplified form after cancellation. Any other form would either reintroduce the canceled factors or would not be equivalent across the domain.

MAT-265-OD24-02-7799

Computing Rational Functions For the given functions and , do the following computation. Choose the best answer. and Find

View Explanation

Log in for full answers

Similar Questions

Find the [math: y] intercept of [math: f(x)=4x2+36x+3+−7] f(x)= \frac{4x^2+3}{6x+3} +-7 Give your answer correct to 2 decimal places.

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)

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

The graph below shows a rational function.Which of the following best describes the graph’s equation, domain, and horizontal asymptote?

Given the following features of a rational function:x-intercept: -2 y-intercept: -3 vertical asymptote: x = 2horizontal asymptote: y = 3 Which of the following is the correct equation?

For which interval is f(x) = \dfrac{1}{x - 2} negative?

The range of 𝑦 = 9 7 − 𝑥

Choose which graph best represents the curve [math: y=4−1x−2]y=4 - \dfrac{1}{x-2} .

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler