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Original problem: x^2-x-20x2-25/x2-16x^2-x-30
Revised: [(x2 - x - 20)(x2 - 25)] / [(x2 - 16)(x2 - x - 30)]
Solution:
Factor the polynomials:
{[(x - 5)(x + 4)][(x + 5)(x - 5)]} / {[(x +4)(x - 4)][(x - 6)(x + 5)]}
Cancel common factors:
[(x - 5)(x - 5)] / [(x - 4)(x - 6)] ---> Simplest form (or final answer)
(Optional) Expand:
(x2 - 10x + 25) / (x2 - 10x + 24)
What else can I help you with?
If the equation of a rational function is a rational expression is the function rational?
Yes. Rational functions must contain rational expressions in order to be rational.
Is there a difference between rational expressions and rational equations?
Yes. An equation has an "=" sign.
After multiplying or dividing two rational expressions it is sometimes possible to the resulting expression?
After multiplying or dividing two rational expressions it is sometimes possible to simplify the resulting expression.
Difference between rational numbers and rational expressions?
A Rational number is a fraction of two integers; a rational expression is a fraction that contains at least one variable
The multiplication property works when the radicands are rational expressions?
true
How are simplifying algebraic expressions similar to simplifying rational expressions?
Simplifying algebraic expressions and simplifying rational expressions both involve reducing the expression to its simplest form by eliminating unnecessary terms or factors. In both cases, you combine like terms and apply properties of operations. For rational expressions, this additionally includes factoring the numerator and denominator to cancel common factors. Ultimately, the goal in both processes is to make the expression easier to work with.
What is a common mistake that is important to avoid when simplifying rational expressions?
Division by a factor that can be zero.
Simplifying trig expressions?
Yes!!! What do you want to know about simplifying trig. expressions.
How are radical expressions related to expressions that contain rational exponents?
Radical expressions and expressions with rational exponents are closely related because they represent the same mathematical concepts. A radical expression, such as √x, can be rewritten using a rational exponent as x^(1/2). Similarly, an expression with a rational exponent, like x^(m/n), can be expressed as a radical, specifically the n-th root of x raised to the m-th power. This interchangeability allows for flexibility in simplifying and manipulating expressions in algebra.
If the equation of a function is a rational expressions the function is rational?
Yes. Rational functions must contain rational expressions in order to be rational.
How can mathematical expressions be solved efficiently?
By simplifying them.
Simplifying rational expressions 6x-5y plus -3x-4y?
(6x - 5y) + (-3x - 4y) =6x - 5y - 3x - 4y =3x - 9y =3 (x - 3y)
Why would you want to factor each expression before multiplying or dividing 2 rational expressions?
In both cases, you may be able to cancel common factors, thus simplifying the expression.
Equations that contain rational expressions?
a rational function.
What is subtraction of rational expressions?
another rational expression.
How do you know if you will subtract or add in simplifying algebraic expressions?
Only like terms can be subtracted or added in algebraic expressions.
How are the sign rules of simplifying expression with rational numbers similar to the sign rules for simplifying expression with integers?
The sign rules for simplifying expressions with rational numbers are similar to those for integers in that they both follow the same basic principles: a positive times a positive is positive, a negative times a negative is positive, and a positive times a negative is negative. This consistency ensures that the operations on rational numbers maintain the same logical structure as those on integers. Consequently, when performing operations like addition, subtraction, multiplication, or division, the sign of the result can be determined using the same rules regardless of whether the numbers involved are rational or integers.
