Question

Solve each equation. $$\frac{6}{t+1}-\frac{34}{15}=\frac{-4}{5 t+5}$$

   Solve each equation.
$$\frac{6}{t+1}-\frac{34}{15}=\frac{-4}{5 t+5}$$

Intermediate Algebra

Intermediate Algebra

John Hornsby; Terry… 13th Edition

Chapter 6, Problem 30

Instant Answer

Solved by Expert Rupsa Sarkar

03/21/2022

Step 1

This gives us: $6(5t+5) - 34(t+1)(5t+5) = -4(t+1)$. Show more…

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Solve each equation. $$\frac{6}{t+1}-\frac{34}{15}=\frac{-4}{5 t+5}$$

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Key Concepts

Rational Equations

Rational equations are equations in which variables appear in the denominators of fractions. Solving them typically requires careful manipulation to combine and eliminate fractions, while also paying attention to potential restrictions in the domain of the variable.

Domain Restrictions

When solving rational equations, it is crucial to identify any values for the variable that would make a denominator zero, as these values are not allowed. Understanding these restrictions helps avoid including extraneous solutions in the final answer.

Common Denominator

A common denominator is used to combine two or more rational expressions into a single expression. Finding a common denominator simplifies the process of adding or subtracting fractions and is an essential step in clearing the fractions from the equation.

Clearing Fractions

Clearing fractions involves multiplying every term in the equation by the least common multiple of the denominators. This step removes the fractions from the equation, making it easier to solve by converting it into an algebraic equation without rational expressions.

Solving Linear Equations

After clearing the fractions, the equation typically reduces to a simpler form such as a linear equation. Solving linear equations involves isolating the variable on one side of the equation through algebraic manipulations like combining like terms and dividing by coefficients.

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