To solve rational expressions, factor the numerator and denominator, cancel common factors, set excluded values, and simplify the result.
Solving rational expressions involves several steps to simplify the expression and find the values of the variable that make the expression undefined.
Here's a step-by-step guide:
Factorization: Factor both the numerator and the denominator completely.
This involves expressing each term as a product of its prime factors.
Cancel Common Factors: Simplify the expression by canceling out common factors between the numerator and denominator.
This helps in reducing the fraction to its simplest form.
Identify Excluded Values: Set the denominator equal to zero and solve for the variable.
The values that make the denominator zero are excluded from the domain because division by zero is undefined.
Express as a Product of Factors: Write the simplified expression as a product of factors.
This can help in identifying any remaining factors that may cancel out.
Check for Extraneous Solutions: If you had to solve an equation to find excluded values, ensure that the solutions are valid for the original expression.
Some solutions may not satisfy the original equation due to the process of squaring or taking roots.
State the Final Simplified Expression: Write down the final simplified expression, including any excluded values.
This expression represents the rational expression in its simplest form.
Question
How do you solve rational expressions step by step?