Question

Find the value of $x .$ $$ \frac{x-1}{x+2}=\frac{10}{3 x-2} $$

   Find the value of $x .$
$$
\frac{x-1}{x+2}=\frac{10}{3 x-2}
$$

Geometry

Ray C.… 1st Edition

Chapter 7, Problem 38

Instant Answer

Solved by Expert Amrita Bhasin

08/30/2019

Step 1

This gives us: \[ (x-1)(3x-2) = (x+2)10 \] Show more…

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Find the value of $x .$ $$ \frac{x-1}{x+2}=\frac{10}{3 x-2} $$

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Key Concepts

Solving Linear Equations

After eliminating fractions, the resulting equation is typically linear, meaning it can be solved by rearranging terms, combining like terms, and isolating the variable. This process involves standard algebraic manipulation steps to reach the solution.

Cross Multiplication

Cross multiplication is a method used to solve proportions or rational equations by multiplying both sides of an equation by the product of the denominators. This technique clears the fractions, transforming the equation into a simpler, often linear form.

Rational Equations

Rational equations are equations in which variables appear in the numerators and denominators of fractions. Solving these equations typically involves finding a common denominator or using techniques such as cross multiplication to eliminate the fractions.

Domain Restrictions

When dealing with rational expressions, it is crucial to identify and exclude any values that cause a denominator to become zero, as these values are not allowed in the domain. This step ensures that the solutions obtained are valid.

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