Let's be rational

It can't get any simpler...or can it?

100

{a+b}/{2b+2a}

1/2

200

{4a-2b}/{b-2a}

-2

300

(a+b)^2/{a^2+b^2}

Cannot be simplified

400

(a-b)^2/{a^2-b^2

{a-b}/{a+b}

500

{b^2-a^2}/{(a-b)^2}

{a-b}/{a+b}

Pluses and Minuses

100

1/a+1/b

{b+a}/{ab}

200

{a-b}/{b-a}-{2c-2d}/{c-d}

1

300

{1-x}/x^2

{1-x}/x^2

400

1/{x^2-y^2)+1/{x-y}

{1+x+y}/{x^2-y^2}

500

1/{x+1}+x/{x-6}-{5x-2}/{x^2-5x-6}

{x-4}/{x-6}

Division Times

100

5/2div1/4

10

200

2/{x^2-4}div1/{x+2}

2/{x-2}

300

{x+2}/{x^2+3x-10}div{x^2-4}/{x^2-25}

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

400

{x^2+5x+6}/{x^2-x-20}times{x^2+3x-4}/{x^2+x-2}

{x+3}/{x-5}

500

(x-y)^2/{y^2+xy}div{y^2-x^2}/{x^2+xy}

{-x(x-y)}/{y(y+x)}

It's complex

100

{1+1/2}/{1-1/3}

9/4

200

{1-1/x}/{1+1/x}

{x-1}/{x+1}

300

{1/x+1/y}/{2+1/{xy}}

{y+x}/{2xy+1}

400

{4-1/{x-1}}/{2+1/{x-1}}

{4x-5}/{2x-1}

500

{3-6/{x+5}}/{1+7/{x-4}}

{3x-12}/{x+5}

Solve it!

100

7-x/2=4

6

200

7-2/x=4

2/3

300

x+x/{x-2}=2/{x-2}

-1

400

x/{x-2}+2/{x+3}=10/{x^2+x-6}

x=-7

500

1/{1-x}=1-x/{x-1}

All real numbers except x=1