What makes a rational equation no solution?

What makes a rational equation no solution?

If a solution is a restriction, then it is not part of the domain and is extraneous. When multiplying both sides of an equation by an expression, distribute carefully and multiply each term by that expression. If all of the resulting solutions are extraneous, then the original equation has no solutions.

Why don t all equations have solutions?

No solution would mean that there is no answer to the equation. It is impossible for the equation to be true no matter what value we assign to the variable. Infinite solutions would mean that any value for the variable would make the equation true. Note that we have variables on both sides of the equation.

Why do rational equations have extraneous solutions?

A rational equation is two rational expressions connected by an equal sign. An extraneous solution to a rational equation is an algebraic solution that would cause any of the expressions in the original equation to be undefined.

How do you tell if a rational equation has no solution?

Be sure to ALWAYS check your answers in the original equation to be sure they do not result in a denominator of zero. If they do, they are not valid answers. If you only have one solution, and it is not valid, then you now have NO SOLUTION.

Can a rational equation have two real solutions?

If the discriminant is a positive number, then there are 2 real solutions. If the discriminant is positive and also a perfect square like 64, then there are 2 real rational solutions.

What is true about rational equations?

When we have an equation where the variable is in the denominator of a quotient, that’s a rational equation. We can solve it by multiplying both sides by the denominator, but we have to look out for extraneous solutions in the process.

Which system of equation has no solution?

inconsistent system of equations
An inconsistent system of equations is a system of equations that has no solution.

Which equations have no solution?

A system of linear equations has no solution when the graphs are parallel. Infinite solutions. A system of linear equations has infinite solutions when the graphs are the exact same line.

When a solution matches an excluded value the solution is called extraneous?

Extraneous solutions are solutions that don’t satisfy the original form of the equation because they produce untrue statements or are excluded values that make a denominator equal to .

Do rational equations always have solutions?

And it is perfectly possible that a given equation will have no solution at all. Whenever you solve a rational equation, always check your (interim) solution against the denominators (and their disallowed values) from the original equation.

What should we know before solving a rational equation?

So before we begin solving a rational equation, we examine it first to find the values that would make any denominators zero. That way, when we solve a rational equation we will know if there are any algebraic solutions we must discard.

Can a rational equation be excluded from the possibilities?

Any solution that makes a denominator in the original expression equal zero must be excluded from the possibilities. A rational equation contains at least one rational expression where the variable appears in at least one of the denominators.

How to find the restrictions in a rational equation?

Since we are solving a rational equation we need to first find the restrictions (the values of x that cause the expression to be undefined). To find the restrictions create an equation by setting each denominator equal to zero and solving.

Why are the numerators of rational equations always the same?

Since the denominator of each expression is the same, the numerators must be equivalent as well.   This means that x = 3. This is true for rational equations with polynomials too: 2x– 5 = 11 x= 8 Again, since the denominators are the same, we know the numerators must also be equal. So we can set them equal to one another and solve for x.