x
−
3
x
2
+
9x
+
20
−
x
−
4
x
2
+
8x
+
15
x
−
3
x
2
+
9x
+
20
−
x
−
4
x
2
+
8x
+
15
size 12{ { {x - 3} over {x rSup { size 8{2} } +9x+"20"} } - { {x - 4} over {x rSup { size 8{2} } +8x+"15"} } } {}
- a. Simplify
- b. What values of
xx are not allowed in the original expression?
- c. What values of xx are not allowed in your simplified expression?
2
x
2
−
1
+
x
x
2
−
2x
+
1
2
x
2
−
1
+
x
x
2
−
2x
+
1
size 12{ { {2} over {x rSup { size 8{2} } - 1} } + { {x} over {x rSup { size 8{2} } - 2x+1} } } {}
- a. Simplify
- b. What values of
xx are not allowed in the original expression?
- c. What values of xx are not allowed in your simplified expression?
4x3−9xx2−3x−10×
2x2−20x+506x2−9x4x3−9xx2−3x−10 size 12{ { {4x rSup { size 8{3} } - 9x} over {x rSup { size 8{2} } - 3x - "10"} } } {}×2x2−20x+506x2−9x size 12{ { {2x rSup { size 8{2} } - "20"x+"50"} over {6x rSup { size 8{2} } - 9x} } } {}
- a. Simplify
- b. What values of
xx are not allowed in the original expression?
- c. What values of xx are not allowed in your simplified expression?
1
x
x
-
1
x
2
1
x
x
-
1
x
2
- a. Simplify
- b. What values of
xx are not allowed in the original expression?
- c. What values of xx are not allowed in your simplified expression?
6x
3
−
5x
2
−
5x
+
34
2x
+
3
6x
3
−
5x
2
−
5x
+
34
2x
+
3
size 12{ { {6x rSup { size 8{3} } - 5x rSup { size 8{2} } - 5x+"34"} over {2x+3} } } {}
- a. Solve by long division.
- b. Check your answer (show your work!!!).
If
f
(
x
)
=
x
2
f(x)=
x
2
, find
f(x+h)−f(x)hf(x+h)−f(x)h size 12{ { {f \( x+h \) - f \( x \) } over {h} } } {}. Simplify as much as possible.
x−12x−1=
x+77x+4x−12x−1 size 12{ { {x - 1} over {2x - 1} } } {}=x+77x+4 size 12{ { {x+7} over {7x+4} } } {}
- a. Solve for xx.
- b. Test one of your answers and show that it works in the original expression. (No credit unless you show your work!)
I am thinking of two numbers,
xx
and
y
y, that have this curious property: their sum is the same as their product. (Sum means “add them”; product means “multiply them.”)
- a. Can you find any such pairs?
- b. To generalize: if one of my numbers is
xx, can you find a general formula that will always give me the other one?
- c. Is there any number
xx that has no possible
yy to work with?
"This is the "main" book in Kenny Felder's "Advanced Algebra II" series. This text was created with a focus on 'doing' and 'understanding' algebra concepts rather than simply hearing about them in […]"