Finding Common Denominators and Expressions

The video tutorial explains how to add rational expressions by first setting up the problem, then using algebraic long division in reverse to multiply expressions and achieve a common denominator. The process involves multiplying the numerator and simplifying the resulting expression. Once a common denominator is established, the rational expressions are added together. The tutorial concludes with a final simplification, demonstrating that no further simplification is possible.

What is the initial expression given in the problem?

• x squared over x squared minus 7x plus 6

• Negative x squared over x squared minus 7x plus 6

• x minus 4 over x squared minus 7x plus 6

• Negative x squared over x minus 4

What is the purpose of multiplying by x squared minus 7x plus 6 over itself?

• To eliminate the denominator

• To find a common denominator

• To simplify the expression

• To change the expression

What is the purpose of the algebraic long division in reverse?

• To simplify the expression

• To find the common denominator

• To change the expression

• To eliminate the denominator

What is the result of multiplying 6 by negative 4?

• 28

• -28

• -24

• 24

What is the new numerator after multiplying the expressions?

• x to the third plus 11x squared plus 34x minus 24

• x to the third minus 11x squared plus 34x minus 24

• x to the third plus 11x squared minus 34x plus 24

• x to the third minus 11x squared minus 34x plus 24

What is the result of x times x squared?

• x to the fifth

• x to the fourth

• x to the third

• x squared

What is the common denominator used in the final expression?

• x squared plus 7x plus 6

• x squared minus 7x minus 6

• x squared minus 7x plus 6

• x squared plus 7x minus 6

What is the final expression after adding the numerators?

• x to the third minus 12x squared plus 34x minus 24

• x to the third plus 12x squared plus 34x minus 24

• x to the third plus 12x squared minus 34x plus 24

• x to the third minus 12x squared minus 34x plus 24

What does the expression factor into?

• x minus 6 times x plus 1

• x plus 6 times x minus 1

• x plus 6 times x plus 1

• x minus 6 times x minus 1

Why is there no further simplification possible?

• Because the expression is already in simplest form

• Because it doesn't factor with the minus 4 in any meaningful way

• Because the expression is too complex

• Because the expression is already factored