Are these algebraic steps correct?
40 - x3
Fail Win!
(Click your answer)
= x + 4 40 3
= 2x + 4
2(4 β 2x) = 3x - 2 2(4) = 5x - 2
Fail Win!
β2βπ₯=2 π₯+3 β2=3 π₯+2Fail Win!
Starter
Are these algebraic steps correct?
Fail Win!
(Click your answer)
π2ππ+π
πππ
Starter
Are these algebraic steps correct?
(x+3)2
Fail Win!
(Click your answer)
x2 + 32
(3x)2
Fail Win!
32x2 9x2
Starter
To cancel or not to cancel, that is the question?
y2 + x2 + x
s(4 + z)s βπ₯2+2=π¦+2
(2x+1)(x β 2)x β 2
pq(r+2) + 1pq
Fail Win! Fail Win!
Fail Win!
Fail Win!
Fail Win!
1 + r2
Fail Win!
- 1
(Click your answer)
Starter
What did we learn?
Bro Tip #1: You canβt add or subtract a term which is βtrappedβ inside a bracket, fraction or root.
Bro Tip #2: In a fraction, we can only divide top and bottom by something, not add/subtract. (e.g. is not the same as !)
Adding/Subtracting Fractions
Whatβs our usual approach for adding fractions?
Sometimes we donβt need to multiply the denominators. We can find the Lowest Common Multiple of the denominators.
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Adding/Subtracting Algebraic Fractions
The same principle can be applied to algebraic fractions.
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Bro Tip: Notice that with this one, we didnβt need to times x and x2 together: x2 is a multiple of both denominators.
Further Examples
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Bro Tip: Be careful with your negatives!
βTo learn the secret ways of the ninja, add fractions you must.β
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Test Your Understanding
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Exercise 1
Harder Questions
3π₯
+ 2π₯β1
=3 (π₯β1 )+2 π₯π₯ (π₯β1 )
= 5π₯β3π₯ (π₯β1 )?
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If were to add say, then we could use 6 as the denominator because is divisible by both 2 and 3.
This gives us a clue what we could use as a denominator .
We can do a cross-multiplication type thing just as before.
2π₯
+ 3π₯+1
=2 (π₯+1 )+3 π₯ π₯(π₯+1)
= 5 π₯+2π₯(π₯+1)
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π₯+1π₯β
π₯π₯+1
=(π₯+1 )2βπ₯2
π₯ (π₯+1 )= 2 π₯+1π₯ (π₯+1 )
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Test Your Understanding
1π₯β1
β3
π₯+3=1 (π₯+3 )β3 ( π₯β1 )
(π₯β1)(π₯+3)= β2 π₯+6
(π₯β1) (π₯+3)? ?
1+1
π₯β1=11+1
π₯β1=
π₯π₯β1? ?
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N1
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Exercise 2
N2 ?
y2
2x3
Γ = xy2
6z2
4x3
= 3z2
4x
x+13
x+24
= 4(x+1)3(x+2)
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Multiplying and DividingThe same rules apply as with normal fractions.
( π₯3
2 )2
=π₯6
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Test Your Understanding
( ) =
x2
243x
Γ = 2x3
x2y3
z5
3 x6y9
z15
2x+13
y+45
= 5(2x+1)3(y+4)?
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y3
2xyΓ = xy2
2
x2y
xyΓ = x2
2y2
x+1x2
xyΓ = x+1
xy
2xy
zq
= 2qxyz
x+1y
z+1q
= q(x+1)y(z+1)
q2
y+1xq
= q3
x(y+1)
( )xy2
= x2
y4
2
( )2q5
z3= 4q10
z6
2
( )3xy
= 9x2
y2
2
( )3x2y3
2z4= 27x6y9
8z12
3
( )x+13y
= (x+1)2
9y2
2
12
( )x+13y
= (x+1)2
9y2
2
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Exercise 3
vs
Head Table
2
3
4 5
6
7
8 9
10
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12 13
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Rear Table
Head To Head
1
π₯2+2
π₯2
Answer:
Question 1
π₯2
+π₯4
Answer:
Question 2
23+π₯+19
Answer:
Question 3
π₯π¦
+π₯+1π¦ 2
Answer:
Question 4
1π₯
+π₯π¦
Answer:
Question 5
1π§
+1
π§+2
Answer:
Question 6
1π₯
+1π¦
+1π§
Answer:
Question 7
1π₯Γ·3
Answer:
Question 8
2Γ·1
π₯2
Answer:
Question 9
1π₯Γ·1
π₯2 π¦
Answer:
Question 10
( π₯π¦ 3 )2
Answer:
Question 11