Page 593 - Algebra 1

Example
4
Dividing Rational Expressions
Find each quotient.
a. 5st÷15st _4 _2
4s2t 2s3t2 SOLUTION
5st ÷15st _4 _2
Math Reasoning
Verify How can you check your solution?
4s2t 2s3t2 5st4 2s3t2
__ = 2 · 2
Write as multiplication by the reciprocal. Multiply the numerators and denominators. Simplify.
Write the polynomial with a denominator of 1. Write as multiplication by the reciprocal. Factor.
Divide out like factors.
Simplify.
_4st 15st 10s4t6
= 60s4t2 _4
= t 6_
b. 9r2 -12r ÷(3r-4) 27
S_OLUTION
9r2 -12r ÷(3r-4)
27
= 9r2 - 12r ÷ (3r - 4) __
27 1
= 9r2 - 12r · 1 __
= 3r(3r - 4) · __
27 (3r - 4)
1
27 (3r - 4)
= 3r(3r - 4) · __
1
= _r 9
c.
x2 +4x+3 ÷ x+3 ___
1
27 (3r - 4) 9
x2 +4x+3 ÷ x+3 ___
x2 x SOLUTION
x2 x = x2 + 4x + 3 · x
___ x2 x+3
Write as multiplication by the reciprocal.
Factor. Divide out like factors. Simplify.
= (x + 3)(x + 1) · x _ _ _1
= _x + 1
x21 (x + 3) x
578 Saxon Algebra 1