How is doing operations (adding, subtracting, multiplying, and dividing) with rational expressions similar to or different from doing operations with fractions? Can understanding how to work with one kind of problem help understand how to work another type? When might you use this skill in real life?
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How is doing operations—adding, subtracting, multiplying, and dividing—with rational expressions similar to or different from doing operations with fractions?
Operations with rational expressions are similar to operations with fractions because rational expressions can be thought of as fractions with variables in the numerator and/or denominator. You can think of rational expressions as algebraic fractions.
When adding or subtracting rational expressions, you need to have a common denominator just like with regular fractions. To get a common denominator, you identify the least common multiple (LCM) of the denominators and then rewrite each rational expression with that common denominator.
When multiplying rational expressions, you simply multiply the numerators together and the denominators together. This is the same as multiplying fractions.
When dividing rational expressions, you can think of it as multiplying by the reciprocal. You take the reciprocal of the second rational expression and then multiply.
Understanding how to work with fractions can definitely help you understand how to work with rational expressions. The concepts and techniques used in working with fractions are very similar to those used in working with rational expressions. For example, finding a common denominator is crucial in adding and subtracting both fractions and rational expressions.
You might use these skills in real life situations that involve problem-solving or simplifying ratios and proportions. For example, when analyzing data or conducting statistical studies, you might need to work with rational expressions to simplify and interpret the results. Additionally, when working with engineering or physics equations that involve variables, you may need to manipulate rational expressions to solve for unknowns.