Simplify Those Rationals!

GCF

100

{12x(x-1)}/22 

{6(x-1)}/11

200

{5x^2(x-5)}/{15x(x+5)}

{x(x-5)}/{3(x+5)}x\ne 0,-5

300

{6ay^3(x-15)}/{4a^2y^3(x+15)(x-1)}

{3(x-15)}/{2a(x+15)(x-1)};x\ne 1,-15

400

{25axz^8(x-12)}/{35a^2xz^3(x+9)}

{5z^5(x-12)}/{7a(x+9)};x\ne 0,-9

Trinomials

100

{x^2-5x+6}/{(x+3)(x-3)}

{(x-2)}/{(x+3)};x\ne -3,3

200

{x^2-18x-81}/{x^2-8x-9}

{(x-9)}/{(x+1)};x\ne -9,1

300

{2x^2-8x+8}/{x^2+10x-12}

{2(x+2)}/{(x+6)};x\ne -6,2

400

{9x^2-18x-27}/{4x^2+12x-72}

{9(x+1)}/{4(x+6)};x\ne 3,-6

DOPS

100

{(x-4)^2}/{x^2-16}

{(x-4)}/{(x+4)};x\ne 4

200

{(x-3)(x+4)}/{6x^2-54}

{(x+4)}/{6(x+3)};x\ne-3,3

300

{9x^2-4a^4}/{(9x-4a^2)(3x-2a^2)}

{(3x+2a^2)}/{(9x-4a^2)} ; xne4/9a^2,2/3a^2

400

{125x^3-45x}/{20(5x+5)(5x-3)}

{x(5x+3)}/{4(x+5)};xne-1,3/5

Potpourri

100

What is the formula for Difference Of Perfect Squares?

a^2-b^2=(a+b)(a-b)

200

{3x^2+18x+24}/{x^2-16}

{3(x+2)}/{(x-4)};xne-4,4

300

{2(x-3)(x+1)}/{(13x+7)+3(x+1)}

{(x-3)(x+1)}/{8x+5};xne-5/8

400

xne?

{x+1}/{x^2-7x+6}

xne1,6