Question

Solve each equation for $x$. $$\frac{x-1}{2 a}=\frac{1}{a-b}$$

   Solve each equation for $x$.
$$\frac{x-1}{2 a}=\frac{1}{a-b}$$

Precalculus

Margaret L. Lial,… 4th Edition

Chapter 1, Problem 54

Instant Answer

Solved by Expert Julie Silva

03/03/2021

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Step 1: We start with the given equation: \[ \frac{x-1}{2a} = \frac{1}{a-b} \] Show more…

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Solve each equation for $x$. $$\frac{x-1}{2 a}=\frac{1}{a-b}$$

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Key Concepts

Variable Restrictions

When working with rational equations, it is crucial to consider the restrictions on the variables. This means identifying any values for the variables that would make a denominator zero, as these values must be excluded from the set of possible solutions to avoid undefined expressions.

Linear Equations

A linear equation is an equation involving only first-degree terms, where the highest power of the variable is one. Once the rational equation is simplified using methods like cross multiplication, the result is often a linear equation in the variable, allowing for straightforward techniques to isolate and solve for the variable.

Rational Equations

Rational equations are equations that involve fractions containing polynomials in the numerator and denominator. Solving these equations typically requires finding a common denominator or using cross multiplication, while also ensuring that any values making a denominator zero are excluded from the solution.

Cross Multiplication

Cross multiplication is a technique used to eliminate fractions from an equation by multiplying each side by the product of the denominators. This process converts the equation into a simpler form, often a linear or polynomial equation, thus making it easier to solve.

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