Solve each equation, if possible. (2)/(y+3)+(3)/(y-4)=(5)/(y+6)

Name: Problem 65, Chapter 1: Algebra and Trigonometry
Uploaded: 2021-06-13T08:41:50-08:00
Duration: 4 min 20 s
Channel: Yujie Wang
Description: Solve each equation, if possible. (2)/(y+3)+(3)/(y-4)=(5)/(y+6)

step 1 Let's look at this problem. So 2 over Y plus 3 plus 3 over 5, y minus 4 equals to 5 over y plus

Solve each equation, if possible....

Key Concepts

Rational Equations

Rational equations are equations that involve rational expressions, which are fractions where the numerator and/or the denominator are algebraic expressions. Solving these equations often involves combining fractions, finding common denominators, and taking into account restrictions on the variable values to avoid division by zero.

Domain Restrictions

When working with rational expressions, it is important to note that any value that makes a denominator equal to zero is not allowed. Identifying these restrictions helps prevent incorrect solutions and ensures that the operations performed during the solving process are valid for the variable’s domain.

Common Denominator

To combine rational expressions effectively, it is often necessary to rewrite them with a common denominator. This process allows addition or subtraction of fractions by ensuring that the expressions share the same denominator, making it possible to combine the numerators directly.

Clearing Denominators

After identifying a common denominator for the terms in the equation, clearing denominators by multiplying both sides of the equation by this common denominator eliminates the fractional expressions. This conversion transforms the rational equation into a simpler algebraic form, typically a linear or polynomial equation, that is easier to solve.

Algebraic Simplification

Once the denominators have been cleared, the resulting equation requires algebraic manipulation such as distributing, combining like terms, and isolating the variable. Simplifying the resulting equation is a critical step to determine the correct solution and check that it adheres to the original domain restrictions.

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