View attached explanation and answer. Let me know if you have any questions.Hello again! Though the original post has the first one only, I have here the works for both problems highlighted with yellow. 😉 As usual, the two files are the answers in two formats (PDF and docx) while the other is for some of the formulas and concepts used. Let me mark this as complete now. For any questions, concerns, clarifications, just send me a message here. 😊

Concepts and Formulas Used
•

Domain of Rational Functions
𝑅(𝑥) =

•

𝑝(𝑥)
, 𝑞(𝑥) ≠ 0
𝑞(𝑥)

Difference of Two Square Formula
𝑎2 − 𝑏 2 = (𝑎 + 𝑏)(𝑎 − 𝑏)


Identify any domain restrictions, the solve the rational polynomial equation. Check your work to verify your answers.
01)
02)

𝑥 2 −4
2𝑥 2 +3𝑥−2
𝑥+1
𝑥+2

+

=1

𝑥+4
𝑥−1

=

𝑥 2 +𝑥+1
𝑥 2 +𝑥−2

Solution:
01)

𝑥 2 −4
2𝑥 2 +3𝑥−2

=1

Domain restrictions:
Denominator cannot be equal to 0.
2𝑥 2 + 3𝑥 − 2 ≠ 0
(2𝑥 2 − 𝑥) + (4𝑥 − 2) ≠ 0
𝑥(2𝑥 − 1) + 2(2𝑥 − 1) ≠ 0
(2𝑥 − 1)(𝑥 + 2) ≠ 0
2𝑥 − 1 ≠ 0, 𝑥 + 2 ≠ 0

2𝑥 − 1 ≠ 0
2𝑥 − 1 + 1 ≠ 0 + 1
2𝑥 ≠ 1
2𝑥 1
≠
2
2
𝑥≠

1
2

𝑥+2≠0
𝑥+2−2≠0−2
𝑥 ≠ −2
𝟏

𝟏

𝟐

𝟐

Domain: (−∞, −𝟐) ∪ (−𝟐, ) ∪ ( , ∞)
Solving the equation:
𝑥2 − 4
=1
2𝑥 2 + 3𝑥 − 2
Factoring 𝑥 2 − 4
𝑎2 − 𝑏 2 = (𝑎 + 𝑏)(𝑎 − 𝑏)
𝑥 2 − 4 = (𝑥 + 2)(𝑥 − 2)
In factored form
(𝑥 + 2)(𝑥 − 2)
=1
(2𝑥 − 1)(𝑥 + 2)

Cancel the ...