Solving and Simplifying Rationals

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Which of the following statements is true when determining excluded values of a rational expression?

• Excluded values are values that make the denominator equal to zero and are found AFTER you cancel like terms from the numerator and denominator.

• Excluded values are values that make the numerator equal to zero and are found AFTER you cancel like terms from the numerator and denominator.

• Excluded values are values that make the denominator equal to zero and are found BEFORE you cancel like terms from the numerator and denominator.

• Excluded values are values that make the numerator equal to zero and are found BEFORE you cancel like terms from the numerator and denominator.

• Flip the first fraction

• Flip the second fraction

• Change the division to multiply

• Flip the second fraction and multiply

• Flip the first fraction and multiply

Is the result rational or irrational? Explain.

• Rational; The sum of two rationals is always rational.

• Irrational; The sum of a rational and an irrational is always irrational.

• Rational; The product of two rationals is always rational.

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Simplify

• (x-9)/(x+9)

• 1/(x-9)

• (x+9)

• 1/(x+9)

Simplify 

• (x+7)/(x-4)

• -3/4

• (x+3)/(x+4)

• (x+3)/(x-4)

Simplify (x² + 3x - 10) / (x² - 1x - 2)

• (x - 5) / (x - 1)

• (x + 5) / (x + 1)

• (x - 2) / (x - 3)

• (x + 2) / (x + 3)

Simplify (x² - 7x + 10) / (x² - 8x + 15)

• (x - 5) / (x - 1)

• (x + 5) / (x + 1)

• (x - 2) / (x - 3)

• (x + 2) / (x + 3)