Exercises 61– 82 involve factoring by grouping (Section 6.1)and factoring sums and differ-
ences of cubes (Section 6.4).Write each rational expression in lowest terms.
83.Concept Check Which two of the following rational expressions equal?
A. B. C. D.84.Concept Check Make the correct choice for the blank: equal to.
(is/is not)
Write each rational expression in lowest terms. See Examples 5 and 6.
5 - x
5 +xp+ 6
p- 6z^2 - 5 z
5 z-z^2q^2 - 4 q
4 q-q^2a^2 - b^2
b-am^2 - 1
1 - m2 - k
k- 26 - t
t- 64 - r - 1
2
4 +r^22 x+ 3- 2 x- 3
2 x+ 3
3 + 2 x2 x- 3
3 - 2 x2 x+ 3
2 x- 3- 1
8 - 27 x^3
27 x^2 + 18 x+ 121 - 8 r^3
8 r^2 + 4 r+ 2t^3 + 64
t^3 - 4 t^2 + 16 tz^3 + 27
z^3 - 3 z^2 + 9 zr^3 + 27
r^2 - 9k^3 + 8
k^2 - 48 y^3 - 27 z^3
9 z^2 - 4 y^2b^3 - a^3
a^2 - b^2r^3 - 1000
r- 10x^3 - 27
x- 38 +x^3
2 +x1 +p^3
1 +py^2 k+pk-y^2 z-pz
yk-yzx^2 y+y+x^2 z+z
xy+xzx^2 - y^2 - 7 y- 7 x
3 x- 3 y- 21m^2 - n^2 - 4 m- 4 n
2 m- 2 n- 8ac-bc-ad+bd
ac-ad-bd+bcac-ad+bc-bd
ac-ad-bc+bdwt+ws+xt+xs
wt-xs-xt+wspr+qr+ps+qs
pr+qr-ps-qskm+ 4 k- 4 m- 16
km+ 4 k+ 5 m+ 20zw+ 4 z- 3 w- 12
zw+ 4 z+ 5 w+ 20- 20 r- 20 r^2 - 5 r^3
24 r^2 + 24 r^3 + 6 r^4 - 3 t+ 6 t^2 - 3 t^3
7 t^2 - 14 t^3 + 7 t^4
2 x^3 + 7 x^2 - 30 x
2 x^3 - 11 x^2 + 15 x3 x^3 + 13 x^2 + 14 x
3 x^3 - 5 x^2 - 28 x3 x^2 + 8 x+ 4
3 x^2 - 4 x- 42 x^2 - 3 x- 5
2 x^2 - 7 x+ 5y^2 - 5 y- 14
y^2 +y- 2x^2 + 2 x- 15
x^2 + 6 x+ 57 t^2 - 31 t- 20
7 t+ 45 k^2 - 13 k- 6
5 k+ 216 x^2 - 9 y^2
12 x- 9 y9 r^2 - 4 s^2
9 r+ 6 s6 t^2 - 6 t
5 t- 53 m^2 - 3 m
5 m- 520 p^2 - 45
6 p- 912 m^2 - 3
8 m- 45 s- 25
s^2 - 252 t+ 6
t^2 - 9a^2 - b^2
a-bm^2 - n^2
m+n5 r+ 20
3 r+ 12SECTION 7.1 The Fundamental Property of Rational Expressions 427