Simplifying Rational Expressions in Elementary Algebra, Slides of Algebra

A list of problems and solutions for simplifying rational expressions, which are essential in algebra and calculus. The problems cover various expression forms, such as fractions with the same or different denominators, and expressions with variables in the numerator and denominator. Understanding these problems and solutions will help build a strong foundation in algebraic manipulations and equation solving.

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2021/2022

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Elementary Algebra Skill
Simplifying Rational Expressions
Simplify each expression.
1)
35
n
35
n
2
2)
45
x
2
25
x
3)
x
− 8
x
2
+
x
− 72 4)
p
2
− 3
p
− 54
p
− 9
5)
56
v
− 72
32
v
6)
a
+ 7
a
2
+ 6
a
− 7
7)
5
v
2
− 5
v
1 −
v
8)
2 −
x
x
2
+ 4
x
− 12
9)
v
2
+ 7
v
− 30
9
v
2
+ 90
v
10)
b
2
+
b
− 30
3
b
2
+ 18
b
11)
3
x
2
+ 5
x
− 2
7
x
2
+ 12
x
− 4 12)
3
b
2
+ 26
b
− 9
5
b
2
+ 40
b
− 45
13)
3
a
2
+ 21
a
− 90
3
a
2
+ 31
a
+ 10 14)
5
m
2
− 57
mn
+ 70
n
2
2
m
2
− 16
mn
− 40
n
2
15)
v
3
+ 11
v
2
+ 18
v
v
2
+
v
− 2 16)
2
x
3
+ 16
x
2
+ 24
x
x
2
x
− 6
17)
xy
+ 3
x
− 2
y
− 6
y
2
+
y
− 6 18)
ax
ay
+
bx
by
ax
ay
bx
+
by
-1-
pf2

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Elementary Algebra Skill

Simplifying Rational Expressions

Simplify each expression.

  1. 35 n 35 n^2
  2. 45 x^

2 25 x

x − 8 x^2 + x − 72

p^2 − 3 p − 54 p − 9

  1. 56 v^ − 72 32 v

  2. a^ + 7 a^2 + 6 a − 7

5 v^2 − 5 v 1 − v

2 − x x^2 + 4 x − 12

  1. v^

(^2) + 7 v − 30 9 v^2 + 90 v

  1. b^

(^2) + b − 30 3 b^2 + 18 b

  1. 3 x^

(^2) + 5 x − 2 7 x^2 + 12 x − 4

  1. 3 b^

(^2) + 26 b − 9 5 b^2 + 40 b − 45

3 a^2 + 21 a − 90 3 a^2 + 31 a + 10

5 m^2 − 57 mn + 70 n^2 2 m^2 − 16 mn − 40 n^2

  1. v^

(^3) + 11 v (^2) + 18 v v^2 + v − 2

  1. 2 x^

(^3) + 16 x (^2) + 24 x x^2 − x − 6

xy + 3 x − 2 y − 6 y^2 + y − 6

axay + bxby axaybx + by

-1-

-2-

Answers to Simplifying Rational Expressions

n

9 x 5

x + 9

  1. p + 6

7 v − 9 4 v

a − 1

  1. −5 v

x + 6

  1. v^ − 3 9 v

  2. b^ − 5 3 b

  3. 3 x^ − 1 7 x − 2

  4. 3 b^ − 1

5 ( b − 1)

( a − 3)

3 a + 1

  1. 5 m^ − 7 n

2 ( m + 2 n )^

  1. v

( v + 9)

v − 1

  1. 2 x

( x + 6)

x − 3

  1. x^ − 2 y − 2

  2. a^ +^ b ab