Page 608 - Algebra 1

z3 - 10z2 4z2 __ __
c. z2 -3z-18 + z2 -3z-18 SOLUTION
z3 - 10z2 4z2 __ __
z2 -3z-18 + z2 -3z-18
= =
z3 - 10z2 + 4z2 __
Add the numerators. Keep the denominator. Combine like terms.
Factor. Divide out common factors.
Simplify.
When the rational expressions being added or subtracted do not have common denominators, use the least common multiple (LCM) to rename each expression.
Adding with Unlike Denominators
Add. Simplify your answers.
2h + 4h _4 _2
6h 2h2
SOLUTION
Rename the expressions so that each has a denominator of 6h2.
z2 - 3z - 18 z - 6z
_3 _2
z2 -3z-18
z (z - 6) _2 _
=
= z + 3
_( z - 6 ) ( z + 3 ) 2
= =
= = =
6h (h )+ 2h2 (3 ) 2h5 12h2
Multiply to get common denominators. 2
z
Example
2
2h + 4h _4 _2
6h 2h2
Hint
Remember to multiply the numerator and denominator by the same value when finding a common denominator.
2h4 _h 4h2 _3 __
_ _ 6h2 + 6h2
Multiply. The LCD is 6h .
Add the numerators. Keep the denominator. Factor and divide out the common factors. Simplify.
2h5 + 12h2 6h2
2h2 (h3 + 6) __
_2h2 (3)
h3 + 6 3
Lesson 90 593