Rational expressions are expressions that involve fractions with polynomials in the numerator and denominator. In mathematics, it is important to be able to simplify and manipulate these expressions to make them equivalent. One way to do this is by filling in the blank with the correct terms to create an equivalent rational expression.
By understanding the rules of algebra and the properties of rational expressions, you can easily simplify and manipulate them to make them equivalent. This skill is crucial in solving equations and problems involving rational expressions.
Fill in the Blank to Make Equivalent Rational Expressions
When simplifying rational expressions, you may need to fill in the blank with the correct term to make them equivalent. For example, if you have the expression (x^2 + 3x + 2) / (x + 2), you can fill in the blank with (x + 1) to make it equivalent to (x + 1)(x + 2) / (x + 2). This simplifies to x + 1, which is equivalent to the original expression.
Another example is if you have the expression (2x^2 – 5x – 3) / (x^2 – 4), you can fill in the blank with (x – 3) to make it equivalent to (2x + 1)(x – 3) / (x – 2)(x + 2). This simplifies to 2x + 1, which is equivalent to the original expression.
It is important to remember that when filling in the blank to make equivalent rational expressions, you must consider the factors of the polynomials and ensure that the expressions are truly equivalent. By practicing this skill, you will become more comfortable with simplifying and manipulating rational expressions.
In conclusion, filling in the blank to make equivalent rational expressions is a valuable skill in algebra and mathematics. By understanding the rules and properties of rational expressions, you can easily simplify and manipulate them to make them equivalent. Practice this skill regularly to improve your algebraic abilities and problem-solving skills.