Algebra

x / (x - 1) = 2

Step-by-step solution with explanation

Final Answer

Step-by-step solution

1

Multiply both sides by denominator

We want to get rid of the fraction. Multiplying both sides by cancels the denominator on the left side.
2

Simplify the left side

The on the left cancels out, leaving just . The right side still needs to be expanded.
3

Distribute on the right side

Multiply by both terms inside the parentheses: and .
4

Move x terms to one side

Subtract from both sides to get all the terms on the left side.
5

Combine like terms and solve

Combining gives . Then divide both sides by to get .
6

Check the answer is valid

Always plug your answer back in to check. Also make sure , since that would make the denominator zero. Since , we are safe.

Understanding this problem

Learning Insight

When you multiply both sides of an equation by an expression, you are using the multiplication property of equality. With rational equations (fractions with variables), this clears the denominator and turns the problem into a simpler linear equation. Always check that your answer doesn't make the denominator zero — those values are called 'excluded values' and can't be solutions.

Quick Tip

Spot a variable in the denominator? Immediately multiply both sides by that denominator to clear the fraction fast. Then solve like a normal linear equation.

Common Mistake

Students often forget to check if the answer makes the denominator equal to zero. For example, if the answer had been , it would make , which is undefined — so it would have to be rejected as a solution.