Solve equation. If a solution is extraneous, so indicate. (a+2)/(a+1)=(a-4)/(a-3)

Name: Problem 73, Chapter 6: Intermediate Algebra
Uploaded: 2020-09-05T05:01:58-08:00
Duration: 2 min 5 s
Channel: Sherrie Fenner
Description: Solve equation. If a solution is extraneous, so indicate. (a+2)/(a+1)=(a-4)/(a-3)

step 1 I have a plus 2 over a plus 1 equals a minus 4 over a minus 3. A cannot equal negative 1 or posi

Solve equation. If a solution is extraneous, so indicate....

Key Concepts

Cross Multiplication

Cross multiplication is a technique used to solve equations involving fractions by multiplying both sides by the denominators, which cancels out the fractions. This results in a simpler algebraic equation that can be solved using standard methods, but it requires careful consideration of any restrictions imposed by the original denominators.

Extraneous Solutions

Extraneous solutions are results obtained during the process of solving an equation that do not satisfy the original equation. They often arise when procedures like cross multiplication are used, which can introduce solutions that make one or more denominators zero. Checking each potential solution against the original equation is necessary to eliminate any extraneous results.

Rational Equations

Rational equations involve expressions that contain ratios of polynomials. Solving these equations requires you to handle potential restrictions in the domain due to denominators that cannot be zero, and often involves cross multiplication to eliminate the fractions and simplify the equation into a more manageable form.

Domain Restrictions

When dealing with rational expressions, it is crucial to identify the values that make any denominator zero. These values are excluded from the solution set because they are not in the domain of the expression. Failure to account for these restrictions may result in invalid or extraneous solutions.

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