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