Precalculus Skill Builders Vol 1 Solutions
Precalculus Skill Builders Vol 1 Solutions
Precalculus Skill Builders Vol 1 Solutions
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11. Algebraic Fractions<br />
Facts about Fractions<br />
PK<br />
QK = P Q<br />
where Q ! 0 and K ! 0<br />
Multiplication:<br />
P<br />
Q ! R S = PR<br />
QS<br />
Division:<br />
P<br />
Q ÷ R S = P Q ! S R = PS<br />
QR<br />
Addition:<br />
Subtraction:<br />
P<br />
Q + R Q = P+R<br />
Q<br />
P<br />
Q ! R Q = P!R<br />
Q<br />
Simplify the following fractions.<br />
1.<br />
1 a<br />
b [ 1 ab ] 2.<br />
1 a<br />
1 b [ b a ]<br />
3.<br />
x 2 –9<br />
x–3 [ x + 3 ] 4. x 2 –5x–6<br />
x 2 –1<br />
5.<br />
x 2 –25<br />
5– x<br />
[ !(x + 5) ] 6.<br />
[ x ! 6<br />
x !1 ]<br />
a 3 +b 3<br />
a 2 –b 2 [ a2 ! ab+ b 2<br />
a! b<br />
]<br />
Example:<br />
Solution:<br />
Use Fraction Busters to solve<br />
x<br />
3 + 5 x = 2 .<br />
Multiply every term on both sides of the<br />
equation by all the terms in the<br />
denominator.<br />
Now you have an equation without<br />
fractions.<br />
Use the Quadratic Formula to solve.<br />
3! x ! x 3 + 3! x ! 5 x = 2 ! 3! x<br />
/3! x ! x /3 + 3! /x ! 5 /x = 6x<br />
x 2 + 15 = 6x<br />
x 2 " 6x + 15 = 0<br />
x=3±i 6<br />
<strong>Skill</strong> <strong>Builders</strong>
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