How to solve a rational equation
What are the steps to solving 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.
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 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 solve equations with rational expressions?
When asked to solve an equation involving rational expressions, you can use either method, whichever one floats your canoe:Eliminate the denominators, or.Write the expression on each side of the equation as a fraction (where the fractions have the same denominator).
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 examples of rational equation?
| Example | |
|---|---|
| Solve | |
| Multiply both sides of the equation by the common denominator. | |
| 7x – 14 + 5x + 10 =10x – 2 12x – 4 =10x – 2 | Simplify |
| 12x – 10x – 4 = 10x – 10x – 2 2x – 4 = -2 2x – 4 + 4 = -2 + 4 2x = 2 x = 1 | Solve for x Check to be sure that the solution is not an excluded value. (It is not.) |
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.
How many solutions can a rational equation have?
That means we have infinitely many solutions. The only value that will not make this equation true is any number that results in a denominator of zero.
What is 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.