Rational equation examples
What is a rational equation?
A rational equation is an equation containing at least one fraction whose numerator and denominator are polynomials, A common way to solve these equations is to reduce the fractions to a common denominator and then solve the equality of the numerators.
How do you write a rational equation?
The steps to solving a rational equation are:Find the common denominator.Multiply everything by the common denominator.Simplify.Check the answer(s) to make sure there isn’t an extraneous solution.
What is the first step in solving a rational equation?
Step 1: Eliminate all fractions. In this case, we can either multiply by the LCD or cross multiply to eliminate the fractions. Step 2: Simplify the resulting equation. To simplify the equation you may need to distribute and combine like terms.
How do you solve rational equations with different denominators?
One way of solving rational equations with unlike denominators is to multiply both sides of the equation by the least common multiple of the denominators of all the fractions contained in the equation. This eliminates the denominators and turns the rational equation into a polynomial equation.
How do you simplify rational equations?
Step 1: Factor both the numerator and denominator of the fraction. Step 2: Reduce the fraction. Step 3: Rewrite any remaining expressions in the numerator and denominator. Step 1: Factor both the numerator and denominator of the fraction.
How do you tell if an equation is rational or irrational?
If you are asked to identify whether a number is rational or irrational, first write the number in decimal form. If the number terminates then it is rational. If it goes on forever, then look for a repeated pattern of digits. If there is no repeated pattern, then the number is irrational.
How do you find the LCD of a rational equation?
To solve a rational equation with the LCD, you find a common denominator, write each fraction with that common denominator, and then multiply each side of the equation by that same denominator to get a nice quadratic equation.
How do you cross multiply rational equations?
Cross multiplication is a process we can use to solve rational equations using the following steps.Simplify the equation to get it in the form a/b = c/d, where a, b, c, and d are numbers, variables, or algebraic expressions.Use cross multiplication to rewrite the equation as ad = bc.Solve the resulting equation.
What are the steps to solving a rational function?
Process for Graphing a Rational FunctionFind the intercepts, if there are any. Find the vertical asymptotes by setting the denominator equal to zero and solving.Find the horizontal asymptote, if it exists, using the fact above.The vertical asymptotes will divide the number line into regions. Sketch the graph.
What is an extraneous solution to a rational equation?
An extraneous solution is a root of a transformed equation that is not a root of the original equation because it was excluded from the domain of the original equation.