- d. = = =
- e. 4 xx= ^14 = 250 , provided that xis not zero.
- b.Any value ofx that makes the denominator
equal to zero, even if it also makes the numer-
ator equal to zero, renders a rational expres-
sion undefined. For the given expression, both
4 and –4 make the denominator equal to zero. - b.Any value ofx that makes the denominator
equal to zero, even if it also makes the numer-
ator equal to zero, renders a rational expres-
sion undefined. To determine these values for
the given expression, we factor the denomina-
tor as x^3 + 3x^2 – 4x= x(x^2 + 3x– 4) = x(x+ 4)
(x– 1). Note that the values –4, 0, and 1 all
make the given expression undefined. - b.
== =
2 xx–+^11- b. = =x
2
4- x
^2
- a. = =
- c. =
= ^39 = ^13 Set 31(Page 79)- a.
+ – =
==- a. + = = =
- d.
- = == = –- d. + = + = =
- c.
- = – = =
=
b. – ^2 t= – = =
- b.
- + ^3 x= - xx+ ^3 x =
==- b.
- + = – + == =
4 x = (2(4xx– 1)(2+ 1)(xx– 1)+ 1)(^2) – 3x– 1
(2x– 1)(2x+ 1)
^2 x^2 – x– 2x– 1 + 2x^2
(2x– 1)(2x+ 1)
x(2x– 1) – 1(2x+ 1) + 2x^2
(2x– 1)(2x+ 1)
^2 x^2
4 x^2 – 1
^2 x+ 1
2 x+ 1
^1
2 x–1
^2 x–1
2 x– 1
x
2 x+ 1
^2 x^2
4 x^2 – 1
^1
2 x– 1
x
2 x+ 1
x^2 + 10x+ 8
x(x+ 1)(x+ 2)
x+ 2 – 2x^2 + 3x^2 + 3x+ 6x+ 6
x(x+ 1)(x+ 2)
x+ 2 – 2x^2 + 3(x+ 1)(x+ 2)
x(x+ 1)(x+ 2)
(x+ 1)(x+ 2)
(x+ 1)(x+ 2)
^2 x
(x+ 1)(x+ 2)
(x+ 2)
(x+ 2)
^1
x(x+ 1)
^2 x
(x+ 1)(x+ 2)
^1
x(x+ 1)
–2
t+ 2
–2t
t(t+ 2)
4 – 2(t+ 2)
t(t+ 2)
2(t= 2)
t(t+ 2)
^4
t(t+2)
^4
t(t+ 2)
^2 x^2 – 3x– 1
x(x– 1)(x– 2)
^2 x– 1 – 5x+ 2x^2
x(x– 1)(x– 2)
2(x– 1) – x(5 – 2x)
x(x– 1)(x– 2)
x
x
5 – 2x
(x– 2)(x– 1)
(x– 1)
(x– 1)
^2
x(x– 2)
5 – 2x
(x– 2)(x– 1)
^2
x(x– 2)
2(2s + r^2 )
s^2 r^3
^4 s+ 2r^2
s^2 r^3
^2 r^2
s^2 r^3
^4 s
s^2 r^3
^2
rs^2
^4
sr^3
^1
x+ 2
–(x– 1)
(x– 1)(x+ 2)
1 – x
( x– 1)(x+ 2)
3 – 2x– (2 – x)
(x– 1)(x+ 2)
2 – x
(x– 1)(x+ 2)
3 – 2x
(x+ 2)(x– 1)
^7
b^3
^7 a
ab^3
^5 a+ 2a
ab^3
^2 a
ab^3
^5 a
ab^3
^3 x– 55
x– 9
^4 x– 45 + 2x– 9 – 3x– 1
x– 9
(4x– 45) + (2x– 9) – (3x+ 1)
x– 9
^3 x+ 1
x– 9
^2 x– 9
x– 9
^4 x– 45
x– 9
(2x– 5)((x+ 4) – (x+ 1))
9(2x– 5)
(2x– 5)(x+ 4) – (2x– 5)(x+ 1)
9(2x– 5)
b^2
2 a+ 1
b^2 (4a– 1)
(4a– 1)(2a+ 1)
^4 ab^2 – b^2
8 a^2 + 2a– 1
^6 x(x^2 – 2)
4 6 xx
^6 x^3 – 12x
24 x^2
(x–1)(5x+ 2)(x– 1)
(x–1)(5x+ 2)(2x+ 1)
(x– 1)(5x^2 – 3x– 2)
(x– 1)(10x^2 + 9x+ 2)
^5 x^2 (x– 1) – 3x(x– 1) – 2(x– 1)
10 x^2 (x– 1) + 9x(x– 1) + 2(x– 1)
x+ 4
x^2 + 5x
(x– 4)(x+ 4)
x(x+ 5)(x– 4)
(x– 4)(x+ 4)
x(x^2 + x–20)
x^2 – 16
x^3 + x^2 – 20x
ANSWERS & EXPLANATIONS–