Test: Algebraic Fractions - Challenging

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Question 1:   Simplify: x3 y+1 y+1 x5
1
x x2
x5 x3
x3 x5
Question 2:   Simplify: x 4 16 x 2 +4
x 2 +4
x 2 12
x 2 4
x2
Question 3:   Simplify: x 2 7x+12 ( x3 )( x+1 )
x3
x3 x+1
x4 x+1
x+1 x4
Question 4:   Simplify: 8 ( x ) 12 x 9
8 x 3
8 x 3
8 x 3
8 x 3
Question 5:   Simplify: x 3 x 1x
x 2 1 x
x 2 1
x( x+1 )
x 2 x
Question 6:   Simplify: 3 x 2 9x 3x
3x
x+3
x3
3x
Question 7:   Simplify: 2 a 2 +8a a 2 16
1 a2
2 a+2
2a a4
4 a+4
Question 8:   Simplify: 3 x : x1 x+1 x 3
x-1 x+1
x+1 x-1
x+1 x1
x
Question 9:   Simplify: 2 x 2 + x x+1
x 3 +2x+2 x 2 ( x+1 )
x 3 +2 x 2 +x+1 x 2 +x+1
x 3 +2 x 2 +1 x 2 ( x+1 )
2+x x 2 +x+1
Question 10:   Simplify: x 2 +2x+1 x+1 + x 2 +x2 x+2
2 x 2 +3x1 ( x+1 )( x+2 )
4 x 2 +3 x 2 +x1 ( x+1 )( x+2 )
2 x 3 +6 x 2 +4x ( x+1 )( x+2 )
3 x 3 +5 x 2 +3x ( x+1 )( x+2 )