3

5. Solve the following rational equations:

a. 𝑥+4𝑥−5

= 𝑥−3𝑥+6

b. 3𝑥𝑥−1

+ 2𝑥𝑥−6

= 5𝑥2−15𝑥+20𝑥2−7𝑥+6

Simplifying Square Roots

Day 1

What’s the difference between a square root and a cube root?

Square Root Cube Root

Let’s learn another way to simplify roots:

1. Simplify the following expressions: a. √𝑥5𝑦73 b. √𝑎13𝑏16𝑐105 c. √𝑘5𝑣9

d. √𝑎6𝑏114 c. √𝑥9𝑦7𝑧53 d. √𝑎21𝑏185

2. So what if throw something in front of it? Simplify: a. 5𝑥𝑦2√𝑥11𝑦133 b. 3𝑎2𝑏4√𝑎12𝑏95 c. 7𝑘𝑣3√𝑘13𝑣11

d. 4𝑎2𝑏5√𝑎7𝑏94 e. 9𝑥4𝑦√𝑥3𝑦5 f. 4𝑎3𝑏2√𝑎8𝑏103

4

3. Find 𝑓(𝑥) − 𝑔(𝑥) and 𝑓(𝑥) + 𝑔(𝑥) for { 𝑓(𝑥) = 8𝑥2 + 9𝑥 − 7

𝑔(𝑥) = 2𝑥2 − 6𝑥 + 23

4. Solve the following equations: a. 𝑥+2

𝑥−3= 𝑥−1

𝑥+3 b. 2(𝑥 + 3)2 − 4 = 36

5. Graph the following functions: a. 𝑦 = 4 ∙ 7𝑥−3 + 1 b. 𝑦 = −2|𝑥 + 3| − 1

Domain: ______________ Domain: ________________

Range: _______________ Range: _________________

5

c. 𝑦 = −√𝑥 + 33 − 5 d. 𝑦 = 5𝑥−4

+ 2

Domain: _______________ Domain: ________________

Range: ________________ Range: _________________

Vertical Asymptote: _______

Horizontal Asymptote: ______

6. Perform the indicated operation:

a. 𝑥2−25𝑥+3

∙ 𝑥2+8𝑥+15𝑥−5

b. 𝑥−4(𝑥+2)(𝑥+5)

÷ 𝑥−4𝑥+5

7. Simplify the following expressions:

a. 3𝑥2𝑦5 ∙ 4𝑥3𝑦2 b. (𝑎3𝑏5)4 c. 𝑥3𝑦5

𝑥7𝑦2

8. Combine Like Terms: 5𝑥𝑦 + 3𝑥2𝑦3 + 3𝑥 + 4𝑦 + 12 + 2𝑥𝑦 + 8𝑥 + 5𝑦 + 4𝑥2𝑦3 + 8