All rational expressions must have restrictions. True or False? Give an example to justify your answer.

Q: - True or False The rational expression (р. 194) 5x – 1 x³ + 1 is proper.

A: Given rational expression is  5x2-1x3+1

Q: Explain how to simplify a rational expression.

A: Rational expression can be simplified by factoring the numerator and denominator and then rewriting…

Q: In Problem,tell whether the given rational expression is proper or improper.If improper,rewrite it…

A: 3x4+x2-2x3+8

Q: If the operation is defined on the set of rational numbers by xy = x + y – 2xy solve the equation x…

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Q: Simplify the rational expression. 2x - 11x-6 - 7x +6 2x - 11x-6 - 7x+6 2

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Q: Give an example of a rational expression with the given restrictions: x + 0, x + -,x # 5. Write the…

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Q: Simplify a rational expression 8x3+4x2/20x

A: Since the given rational expression is not clear, it has been solved in two cases.

Q: Simplify the rational expression. x3-343 3x-21

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Q: Rewrite as equivalent rational expressions with denominator (x– 2)(x – 5)(x – 6). - 7 4x x2 – 7x +…

A: 7x2-7x+10,4xx2-8x+12

Q: Create a presentation that could be used to teach a student how to add, subtract, multiply, and…

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Q: In Problem,tell whether the given rational expression is proper or improper.If improper,rewrite it…

A: given,       5x3+2x-1x2-4

Q: Find all numbers that must be excluded from the domain of the rational expression : 7 / (x - 3)

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Q: Simplify the rational expression.

A: Given: 5(x-3)(2x+1)10(x-3)2Description: terminate the common factor both in the numerator and in the…

Q: The rational expression (x3 + 2x2 − 7x + 4) / (x2 − 4x − 12) is improper.Determine whether the…

A: A rational fraction in which degree of numerator is greater than or equal to degree of the…

Q: Find all numbers that must be excluded from the domain of the rational expression : (x +7) / (x2 -…

A: The denominator can never be 0. Because division by 0 is undefined.

Q: Rewrite the expression as a single rational expression. + x – 1

A: Given: 1xx-1+x-1 To Find: Rewrite the expression as a single rational expression

Q: Simplify  rational expression (x3 + 2x2)/(x + 2). Also, list all numbers that must be excluded from…

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Q: Write the rational expression in simplest form. x2 - 81 x3 + x 2 - 81x - 81

A: Given that  Expression  (x^2-81)/(x^3+x^2-81x-81) To simplify the expression

Q: How to Simplify a rational expression? Explain with examples.

A: Rational expression:

Q: Find all numbers for which the rational expression is undefined -En

A: The given rational expression is n3-6nn2-4.

Q: Explain how to simplify rational expressions

A: We have to write the steps for simplify rational expressions.

Q: Which rational expressions are equivalent to −x/y​?

A: Consider the expression  -xy

Q: State the restricted values of the rational expression: 3x-5/4x-8

A: Given query is to find the restricted values for the function.

Q: Explain why it is necessary to checkthe possible solutions of a rational equation

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Q: Find the least common denominator of the rational expressions.

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Q: 5x +x²-8x 2- メレ

A: Calculation are as follows

Q: -4 x' +5x +6 x +3x 2x +4 2x +4 x +3x

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Q: Drag the appropriate expression to complete the first step for writing an equivalent rational…

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Q: Write the rational expression in simplest form. 2 - 36 6 - X

A: We Know that A rational expression is considered simplified if the numerator and denominator have no…

Q: A rational expression is the quotient of two___________.

A: we know that A rational expression is the quotient of two polynomials

Q: Simplify  rational expression (x2 + 2x)/(x2 + 4x + 4). Also, list all numbers that must be excluded…

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Q: Rewrite as equivalent rational expressions with denominator (3x + 3)(x – 6)(x – 9). 8x 3x2 15x –…

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Q: Find all numbers for which the rational expression is undefined.

A: The rational expression is undefined when the denominator of the rational expression becomes equal…

Q: Add the rational expressions. 7/2x(x+2) + x+3/x+2

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Q: Is the set of rational expressions closed under subtraction? Explain p(x) r(x) %3D (x)b s(x) II

A: Topic = Polynomials

Q: What is the value of the discriminant whose root are real,rational,and equal?

A: Given: - The discriminant whose roots are real, rational, and equal. To find: - The value of the…

Q: Simplify the rational expression. 2x - 3x- 2 6x + 3x + 2x+ 1

A: 2x2-3x-26x3+3x2+2x+1=2x2-4x+x-23x2(2x+1)+2x+1=2x(x-2)+1(x-2)(2x+1)(3x2+1)=(x-2)(2x+1)(2x+1)(3x2+1)=(…

Q: I use the fact that 1 is the multiplicative identity to both rationalize denominators and rewrite…

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Q: 9- 4x x+7 x+10x+21

A: Explained below

Q: Write the rational expression in simplest form. + 4x - 12 x2 + 7x + 6

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Q: Reduce the  rational expression to lowest terms (3x + 9) / (x2 - 9)

A: Reduce the  rational expression to lowest terms     3x+9x2-9

Q: Find all numbers that must be excluded from the domain of  rational expression. [(x + 7/x2 - 49)]

A: Consider the following rational expression: x+7x2-49 Denominator of rational function should not be…

Q: write the rational expression in lowest term. xy-2x+5y-10/xy+3x+5y+15

A: Given rational expression is,

Q: Reduce the  rational expression to lowest terms ( 2x2 + 5x - 3 ) / ( 1 - 2x )

A: The given rational expression is, 2x2+5x-31-2x To reduce the given rational expression, we factorize…

Q: 2-6 2-3x X-2 X-2

A: Explanation of the solution is given below...

Q: Reduce the  rational expression to lowest terms (x2 + 4x + 4)/ x2 - 4

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Q: Simplify the rational expression 2x-6x^2/2x

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Q: Write a rational expression that is undefined for x = -10

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Q: Simplify the rational expression.

A: Given: The expression x-2x2-4, To find: The simplified expression of the given expression.

Q: Reduce the rational expression to lowest terms. 2p² + 12p+16 2 4p²-4p-80 2p² +12p+16 4p²-4p-80

A: I am attaching image so that you understand each and every step.