Solve equation, and check your solutions. (2)/(p+3)+(3)/(8)=(5)/(4 p+12)

Name: Problem 56, Chapter 6: Beginning and Intermediate Algebra
Uploaded: 2020-07-19T18:56:19-08:00
Duration: 2 min 57 s
Channel: Grace Muhihu
Description: Solve equation, and check your solutions. (2)/(p+3)+(3)/(8)=(5)/(4 p+12)

step 1 Okay, so to solve this equation, first I'm going to need all common denominators. So in this cas

Solve equation, and check your solutions....

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Key Concepts

Clearing Denominators

A common method for simplifying rational equations is to eliminate the fractions by multiplying every term by the least common denominator (LCD). This procedure simplifies the equation to a form without fractions, which is usually easier to solve, though care must be taken not to introduce extraneous solutions.

Extraneous Solutions Check

After solving the simplified equation, it is essential to check each potential solution in the original equation. This step verifies that none of the candidate solutions make any denominator zero and that the solution truly satisfies the original rational equation.

Rational Equations

Rational equations are equations that involve fractions with polynomials in their numerators and denominators. Solving these types of equations often requires careful manipulation to combine and simplify the fractional expressions, keeping in mind that the variable appears in the denominators.

Domain Restrictions

When dealing with rational equations, it is important to identify values for which the original expressions are undefined. This typically involves setting each denominator that contains the variable not equal to zero, thereby ensuring that the solutions lie within the domain of the original equation.

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