Question

Solve each equation. $$ \frac{x-7}{x-1}=\frac{11}{x-1} $$

   Solve each equation.
$$
\frac{x-7}{x-1}=\frac{11}{x-1}
$$

Intermediate Algebra

Intermediate Algebra

Elayn Martin-Gay 6th Edition

Chapter 6, Problem 10

Instant Answer

Solved by Expert Charles Carter

07/16/2020

Step 1

So, we set $x-1$ not equal to zero: $$x-1 \neq 0$$ Solving for $x$, we find that $x \neq 1$. Show more…

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Solve each equation. $$ \frac{x-7}{x-1}=\frac{11}{x-1} $$

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Key Concepts

Domain Restrictions

When dealing with rational expressions, it is crucial to identify the values of the variable that cause any denominator to equal zero. These values are excluded from the solution set because they render the expression undefined. Careful consideration of these restrictions helps avoid obtaining extraneous solutions.

Equating Numerators When Denominators Are Equal

In cases where both sides of an equation have the same nonzero denominator, the equality of the fractions implies that the numerators must be equal. This approach simplifies the process by allowing you to focus on solving a simpler equation derived from the numerators while ensuring that the common denominator is not zero.

Rational Equations

A rational equation is one that involves rational expressions, which are fractions where the numerator and/or the denominator are polynomials. Solving these equations usually involves finding a common denominator and then eliminating the fractions to simplify the equation into a form that can be solved with common algebraic methods.

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