Series: Rational Expressions
In this video we learn how to add and subtract rational expressions, which are just fractional expressions in which the numerator and denominator are both polynomials. Just like with simple fractions, we have to find a common denominator in order to add the fractions together or subtract one fraction from another. We'll find a common denominator among the fractions (which will be the lowest common multiple of the denominators), and then combine the fractions. Show Less
In this video we learn how to divide rational expressions, which are fractional expressions in which both the numerator and denominator are polynomials. We'll turn the division problem into a multiplication problem by taking the reciprocal of the divisor and switching the division to multiplication. Before we do the multiplication, we should factor the numerator and denominator of both fractions as much as we can in order to see if there's anything we can cancel within either fraction or across both fractions. Show Less
Learn how to use polynomial long division to simplify a rational function, which is the quotient, or fraction, of two polynomials. This will work the same way as long division with real numbers. The numerator goes on the inside of the long division problem; the denominator goes on the outside. Figure out what you have to multiply by the first term from the numerator to get the first term from the denominator. Put this above the first term from the denominator, then multiply this value by the entire denominator, writing the result below the numerator. Subtract the value from the numerator, carry down the next value, and repeat this process. Show Less
In this video we learn how to multiply rational expressions, which are fractions that have a polynomial in both the numerator and denominator. Before we do the multiplication, we'll try to factor the numerators and denominators as much as possible, and then see if we can cancel any factors within either fraction or across the fractions. Once we've cancelled as much as possible, then we'll do the multiplication. Show Less
In this video we'll learn how to simplify rational functions by reducing them to their lowest terms by cancelling common factors.