Find the real solutions of each equation. (1)/((x+1)^2)=(1)/(x+1)+2

Name: Problem 67, Chapter 1: College Algebra
Uploaded: 2020-04-17T08:38:11-08:00
Duration: 2 min 59 s
Channel: Ankit Gupta
Description: Find the real solutions of each equation. (1)/((x+1)^2)=(1)/(x+1)+2

step 1 given equation is 1 divided by x plus 1 whole square equal to 1 divided by x plus 1 plus 2 now l

Find the real solutions of each equation....

Key Concepts

Rational Equations

Rational equations are equations that involve fractions where the numerator and/or the denominator contains a variable. Solving these equations typically requires finding a common denominator or multiplying through by an appropriate expression to eliminate the fractions, while keeping in mind the restrictions on the variable values that make the denominators nonzero.

Domain Restrictions

Domain restrictions refer to the limitations placed on the variable values in an equation, often due to the presence of denominators or square roots. When solving rational equations, it is important to exclude any values that would make a denominator zero or otherwise lead to undefined expressions in the equation.

Substitution Method

The substitution method is a technique used to simplify the equation by replacing a recurrent complicated expression with a temporary variable. This approach reduces the original equation to a simpler form, such as a quadratic equation, which is easier to solve.

Clearing Denominators

Clearing denominators involves multiplying both sides of a rational equation by the least common denominator of all the fractions present in the equation. This step eliminates the fractions and converts the equation into a polynomial equation, facilitating further algebraic manipulation.

Quadratic Equation

A quadratic equation is a polynomial equation of degree two. After simplifying a rational equation, it often results in a quadratic form which can be solved using methods such as factoring, completing the square, or applying the quadratic formula. Determining the roots of the quadratic equation is a key step in finding the solutions to the original problem.

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