Reduce Fractions with polynomials

CONCEPTS

Tips

• Use the distributive property &/or factor the equations in both the numerator & denominator

• Find the LCD or least common denominator to add fractions

• Reduce fraction by canceling terms

PRACTICE PROBLEMS

Question 1 Simplify

-- Answer -- 9x + 36 / / ((x – 3)(x + 3)(x + 6))

3 / ((x – 3)(x + 3)) + 6 / ((x + 6)(x – 3))

The common denominator = (x – 3)(x + 3)(x + 6)

3 / ((x – 3)(x + 3)) * (x + 6)/(x + 6) + 6 / ((x + 6)(x – 3)) * (x + 3)/(x + 3)

= 3 * (x + 6) / ((x – 3)(x + 3)(x + 6)) + 6 * (x + 3) / ((x – 3)(x + 3)(x + 6))

= 3x + 18 + 6x + 18 / ((x – 3)(x + 3)(x + 6))

= 9x + 36 / / ((x – 3)(x + 3)(x + 6))

ACT PRACTICE PROBLEMS