Rewriting Rational Expressions
Algebra 2 · Flashcards
ALGEBRA 2 · FLASHCARDS
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QUESTION
What identity rewrites
a
(
x
)
a(x)
a
(
x
)
after division by
b
(
x
)
b(x)
b
(
x
)
?
QUESTION
What is
6
x
2
+
7
x
−
3
3
x
+
1
\frac{6x^2+7x-3}{3x+1}
3
x
+
1
6
x
2
+
7
x
−
3
rewritten as
q
(
x
)
+
r
(
x
)
3
x
+
1
q(x)+\frac{r(x)}{3x+1}
q
(
x
)
+
3
x
+
1
r
(
x
)
?
QUESTION
What is
x
3
−
1
x
−
1
\frac{x^3-1}{x-1}
x
−
1
x
3
−
1
rewritten as
q
(
x
)
+
r
(
x
)
x
−
1
q(x)+\frac{r(x)}{x-1}
q
(
x
)
+
x
−
1
r
(
x
)
?
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ANSWER
x
2
+
x
+
1
+
0
x
−
1
x^2+x+1+\frac{0}{x-1}
x
2
+
x
+
1
+
x
−
1
0
. Use identity
x
3
−
1
=
(
x
−
1
)
(
x
2
+
x
+
1
)
x^3-1=(x-1)(x^2+x+1)
x
3
−
1
=
(
x
−
1
)
(
x
2
+
x
+
1
)
for exact division.
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