What is the meaning term rational expression. In your word and examples explain how to divide rational expressions
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A rational expression is an expression in the form of a fraction that involves polynomials in the numerator and denominator. It can be seen as a division of two polynomials.
To divide rational expressions, follow these steps:
Step 1: Simplify both the numerator and denominator as much as possible.
Step 2: Flip the second rational expression (the one you want to divide by) and convert it into its reciprocal. In other words, interchange the numerator and denominator.
Step 3: Now that you have the reciprocal, you can multiply the first rational expression by the reciprocal.
Step 4: Simplify the resulting expression by multiplying the numerators together and multiplying the denominators together.
Here is an example to help illustrate the process:
Divide: (3x^2 - 5x + 2) / (2x + 1) by (x - 2)
Step 1: Simplify the numerator and denominator if possible:
(3x^2 - 5x + 2) cannot be factored any further, and (2x + 1) and (x - 2) cannot be simplified.
Step 2: Flip the second rational expression (the divisor) to find its reciprocal:
(x - 2) becomes (1 / (x - 2))
Step 3: Multiply the first rational expression by the reciprocal:
(3x^2 - 5x + 2) * (1 / (x - 2))
Step 4: Simplify the resulting expression by multiplying the numerators and denominators:
((3x^2 - 5x + 2) * 1) / ((2x + 1) * (x - 2))
Final Result: (3x^2 - 5x + 2) / (2x^2 - 3x - 2)
Remember to always check for restrictions in the domain, such as values of x that make the denominator zero.