Question

Solve each equation. $n+\frac{1}{n}=\frac{37}{6}$

Name: Problem 16, Chapter 4: Intermediate Algebra
Uploaded: 2022-03-03T17:13:49-08:00
Duration: 39 s
Channel: Victor Salazar
Description: Solve each equation. n+(1)/(n)=(37)/(6)

   Solve each equation.
$n+\frac{1}{n}=\frac{37}{6}$

Intermediate Algebra

Jerome E. Kaufmann,… 10th Edition

Chapter 4, Problem 16

Instant Answer

Solved by Expert Victor Salazar

03/03/2022

Step 1

This gives us: \[n^2 + 1 = \frac{37n}{6}\] Show more…

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Solve each equation. $n+\frac{1}{n}=\frac{37}{6}$

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Key Concepts

Quadratic Equations

Many rational equations, once cleared of fractions, become quadratic equations. Quadratic equations are polynomial equations of degree two that can be solved using various methods such as factoring, completing the square, or applying the quadratic formula. This concept is essential when the resulting equation after clearing denominators is quadratic in form.

Rational Equations

Rational equations involve expressions where the variable appears in the denominator. Solving these equations typically requires identifying any restrictions on the variable (such as values that make the denominator zero) and then manipulating the equation to eliminate the fractions.

Clearing Denominators

Clearing denominators is a technique used to simplify rational equations. By multiplying every term in the equation by a common denominator, the equation is transformed from a rational equation into a polynomial equation, which is usually easier to solve.

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