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 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.
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 a rational quadratic equation?
Solutions to Quadratic Equations With Rational ExpressionsThe given equation. x 2 + 2x = -1.Write the above quadratic equation with right side equal to 0. x 2 + 2x + 1 = 0.Factor the equation. (x + 1) 2 = 0.Solve the equation to obtain the repeated solution. x = -1.
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 solve rational equations with LCD?
Solve Rational Equations Using Their LCDFind a common denominator for all the terms in the equation. Write each fraction with the common denominator. Multiply each side of the equation by that same denominator. Solve the new equation. Check your answers to avoid extraneous solutions.
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.
How are rational equations used in real life?
Rational equations can be used to solve a variety of problems that involve rates, times and work. Using rational expressions and equations can help you answer questions about how to combine workers or machines to complete a job on schedule.