Rationals

Addition

100

((u-v)/8v) + ((6u-3v)/8v)

((7u-4v)/8v)

200

(r+6)/(3r-6)+(r+1)/(3r-6)

(2r+7)/(3r-6)

300

(7n)/(n+1) + 8/(n-7)

(7n²-41n+8)/((n+1)(n-7))

400

(3)/(x+7)+(4)/(x-8)

(7x+4)/((x-8)(x+7))

500

(5n+5)/(5n²+35n-40)+(7n)/(3n)

(52n-53+7n²)/(3(n+8)(n-1))

Subtraction

100

(8n)/(n+8)-(7)/(n+8)

(8n-7)/(n+8)

200

((x+2)/2x²+13x+20) - ((x+3)/2x²+13x+20) 

-((1)/2x²+13x+20) 

300

((6)/x-1) - ((5x)/4)

(24-5x²+5x)/4(x-1)

400

(4)/(x+1)-(2)/(x+2)

(2x+6)/((x+1)(x+2))

500

(7/3)-8/(12x-8)

(21x-20)/(3(3x-2))

Multiplication

100

(8(m+1)/7m)*(9/8(m+1))

9/7m

200

6(r+2)/20*((4r)/6(r+2))

r/5

300

1/(v+10)*(10v+30)/(v+3)

10/(v+10)

400

(x+7)/(7x+35)*((x²-3x-40)/(x-8))

(x+7)/7

500

(6n+6)/(n+9)*((n²+6n-27)/(6n+6))

n-3

Division

100

5/20)/(5x/3

3/20x

200

(3/28b)/(3/(b+1))

(b+1)/28b

300

6/(28x+4)/(6/(35x+5))

5/4

400

(x²+10x+16)/(x²+6x+8)/(1/(x+4))

x+8

500

(6p+27)/(18p²+36p)/((16p+72)/(2p+4))

1/24p

Solving

100

1/6k²=1/3k² - 1/k

1/6

200

(r-4)/5r=1/5r + 1

-5/4

300

(r+5)/(r²-2r)-1=1/(r²-2r)

4,-1

400

1/(x²-5x)=(x+7)/x)-1

36/7

500

(a-2)/(a+3)-1=3/(a+2)

-19/8