Rational Expressions and EquationsA series of free Basic Algebra Lessons from Brightstorm online Algebra series.
Multiplying and Dividing Rationals Multiplying rational expressions is basically two simplifying problems put together. When multiplying rationals, factor both numerators and denominators and identify equivalents of one to cancel. Dividing rational expressions is the same as multiplying with one additional step: we take the reciprocal of the second fraction and change the division to multiplication.
Dividing Polynomials Long division can be used to divide a polynomial by another polynomial, in this case a binomial of lower degree. When dividing polynomials, we set up the problem the same way as any long division problem, but are careful of terms with zero coefficients. For example, in the polynomial x3 + 3x + 1, x2 has a coefficient of zero and needs to be included as x3+ 0x2+3x+1in the division problem.
Adding and Subtracting Rational Expressions Adding and subtracting rational expressions is similar to adding fractions. When adding and subtracting rational expressions, we find a common denominator and then add the numerators. To find a common denominator, factor each first. This strategy is especially important when the denominators are trinomials.
Solving Rational Equations
Solving Rational Equations with Unlike Denominators When solving rational equations with unlike denominators, the first step is to factor the denominators and look for a common denominator. Next, we multiply both sides of the equation by the common denominator to clear the fractions. Finally, we solve for the variable using an appropriate technique.
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