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When is rational expression undefine or meaningless?
A rational number is any number that can be expressed as a fraction. It becomes meaningless or undefined when the lower number, the denominator, its 0 (zero)
How do you solve rational expressions?
To solve rational expressions, first, factor both the numerator and the denominator whenever possible. Next, identify any common factors that can be canceled out to simplify the expression. If the expression includes an equation, set the simplified form equal to zero to find the variable's value, and ensure to check for any excluded values that make the denominator zero. Finally, express the solution in its simplest form.
What situation would one or more solutions of rational equation be unacceptable?
Whenever you solve a rational equation you must make sure the result obtained for an answer does not allow the denominator of one of the rational expressions to assume a value of ZERO, as division by zero is undefined and therefore prohibited. For example if we have 2x/(x-3) =(x2 -9x)/ x when we multiply out by x(x-3) we get 2x(x) = (x2 -9x)(x-3) so 2x2 = x(x-9)(x-3) 2x2 = x(x2 - 12x + 27) 2x2 = x3 - 12x2 + 27x so 0 = x3 - 14x2 + 27x 0 = x(x2 - 14x + 27) so solutions are 0 and 7 + √22 and 7 -√22 but 0 makes right hand side expression have zero in denominator so it is not a solution. We actually have to look at all obtained solutions to be sure they ae not extraneous. Suppose we had obtained a 3 for a solution. That would make the left side denominator equal zero and we would have to dismiss that, if 3 was obtained. The two irrational solutions we have obtained are genuine solutions as neither introduces a zero to a denominator
What does fractional index mean?
A power with a rational exponent m/n in lowest terms satisfies : whenever this makes sense.
Rational and irrational numbers are complex numbers?
Rational and irrational numbers are real numbers. A complex number is represented by a+bi where a and b are real numbers. Zero is a real number therefore any real number is also complex whenever b=0
A rational expression is undefined whenever its denominator is zero-?
True
How do you determine the values for which a rational expression is undefined?
A rational expression is not defined whenever the denominator of the expression equals zero. These will be the roots or zeros of the denominator.
A rational expression is undefined whenever its denominator is zero?
False
When is rational expression undefine or meaningless?
A rational number is any number that can be expressed as a fraction. It becomes meaningless or undefined when the lower number, the denominator, its 0 (zero)
A rational expression is undefined whenever its numerator is zero?
false
Is a rational expression undefined whenever its number is zero?
No. 0/3 is well defined.
When do use denominator in the real world?
Whenever we are dealing with rational fractions.
How do you solve rational expressions?
To solve rational expressions, first, factor both the numerator and the denominator whenever possible. Next, identify any common factors that can be canceled out to simplify the expression. If the expression includes an equation, set the simplified form equal to zero to find the variable's value, and ensure to check for any excluded values that make the denominator zero. Finally, express the solution in its simplest form.
What situation would one or more solutions of rational equation be unacceptable?
Whenever you solve a rational equation you must make sure the result obtained for an answer does not allow the denominator of one of the rational expressions to assume a value of ZERO, as division by zero is undefined and therefore prohibited. For example if we have 2x/(x-3) =(x2 -9x)/ x when we multiply out by x(x-3) we get 2x(x) = (x2 -9x)(x-3) so 2x2 = x(x-9)(x-3) 2x2 = x(x2 - 12x + 27) 2x2 = x3 - 12x2 + 27x so 0 = x3 - 14x2 + 27x 0 = x(x2 - 14x + 27) so solutions are 0 and 7 + √22 and 7 -√22 but 0 makes right hand side expression have zero in denominator so it is not a solution. We actually have to look at all obtained solutions to be sure they ae not extraneous. Suppose we had obtained a 3 for a solution. That would make the left side denominator equal zero and we would have to dismiss that, if 3 was obtained. The two irrational solutions we have obtained are genuine solutions as neither introduces a zero to a denominator
Does the denominator ever change?
Yes it does: whenever you find an equivalent fraction.
Why does Tom Cruise only act with one facial expression?
cause whenever he sees little boys he makes that facial expression
Is negative pi rational or irrational?
-Pi is irrational, because it does not terminate or repeat. Whenever you multiply an irrational number by a rational number (-1), the result is an irrational number.
