Question

Solve each equation. $$ \frac{x}{x+2}=\frac{3}{2} $$

   Solve each equation.
$$
\frac{x}{x+2}=\frac{3}{2}
$$

College Algebra

College Algebra

Michael Sullivan 10th Edition

Chapter 1, Problem 55

Instant Answer

Solved by Expert Ankit Gupta

04/28/2020

Step 1

This gives us: $$x = \frac{3}{2}(x+2)$$ Show more…

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Solve each equation. $$ \frac{x}{x+2}=\frac{3}{2} $$

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Key Concepts

Rational Equations

Rational equations are equations that contain one or more rational expressions, where numerators and denominators are polynomials. Solving these equations typically involves finding a common denominator or using techniques such as cross multiplication to eliminate fractions and simplify the equation into a polynomial form.

Domain Restrictions

When working with rational expressions, it is essential to consider the domain restrictions imposed by the denominators. Values that lead to a zero denominator are not allowed, as division by zero is undefined, and these potential solutions must be excluded from the final answer.

Cross Multiplication

Cross multiplication is a technique often used to solve equations that set two fractions equal to each other. It involves multiplying the numerator of one fraction by the denominator of the other, thereby eliminating the fractions and resulting in a simpler, typically linear or polynomial equation.

Linear Equations

After applying techniques such as cross multiplication to a rational equation, the resulting equation is often a linear equation. Solving a linear equation involves isolating the variable through operations like addition, subtraction, multiplication, and division to determine the value of the variable.

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