Simplifying Algebraic Fractions

Factors with exponents

100

12(x-2)³(2x-5)⁴

_______________

18(2x-5)²(x-2)

2(x-2)²

_________

3(2x-5)

200

36(y-7)⁴(3y-8)⁴

_______________

40(3y-8)⁵(y-7)

9(y-7)³

_______________

10(3y-8)

300

36(v-7)⁵(3v-8)⁴

_______________

45(3v-8)⁵(v-7)

4(v-7)⁴

^___________

5(3v-8)

400

12v⁵(v+8)²(2v+5)

_______________

30v³(v+8)³

2v²(2v+5)

_______________

5(v+8)

500

36w³(w+6)³

________________

27w⁵(w+6)²(2w+5)

4(w+6)

__________

3w²(2w+5)

GCF factoring

100

18v²-42v

________

6v²-48v

3v-7

_____

v-8

200

12y²-16y

________

4y²-8y

3y-4

____

y-2

300

3v²-21v

________

4v²-28v

3

_

4

400

7x+49

______

6x²+42x

7

__

6x

500

5x²-30x

________

6x²-36x

5

_

6

Quadratic LC = 1

100

v²-4

____

v+2

v-2

200

v²+12v+36

__________

v+6

v+6

300

u²+9u+14

__________

u+7

u+2

400

u-8

___________

u²-64

1

_____

u+8

500

x-2

____

x²+3x-10

1

___

x+5

Ratio of polynomials: Problem Type 1

100

y²-5y-6

________

4y²-4

y-6

_______

4(y-1)

200

y²+2y-15

__________

4y²-36

y+5

_____

4(y+3)

300

5u²-45

__________

u²-2u-15

5(u-3)

______

u-5

400

v²-v-2

________

5v²-20

v+1

________

5(v+2)

500

v²-4v-21

_________

4v²+32v+60

v-7

_______

4(v+5)

Ratio of polynomials: Problem Type 3

100

v²+6v-7

__________

3v²+16v-35

v-1

_____

3v-5

200

9y²-1

________

3y²+20y-7

3y+1

_______

y+7

300

7x²+23x+6

_________

49x²-4

x+3

_____

7x-2

400

v²+2v-15

_________

5v²+24v-5

v-3

____

5v-1

500

x²-3x-10

_________

5x²+3x-14

x-5

_____

5x-7