1. x/x+3 + x+2/x+5

2. x+4/x2+5x+6 • x+3/x2-16

3. 2/x2-9 - 3x/x2-5x+6

4. x+4/x2-5x+6 : x2-16/x+3

Show your work

1. x = √ (73) / 2 - 9/2 or x = - 9/2 - √ (73) / 2

2. x = (512 2^ (1/3) + (18 i √ (16303) + 16222) ^ (2/3)) / (6 (9 i √ (16303) + 8111) ^ (1/3)) + 16/3 or x = 16/3 + (256 (-1) ^ (2/3)) / (3 (1/2 (9 i √ (16303) + 8111)) ^ (1/3)) - 1/3 ((-1) / 2) ^ (1/3) (9 i √ (16303) + 8111) ^ (1/3) or x = ((-2) ^ (2/3) (9 i √ (16303) + 8111) ^ (2/3) - 512 (-2) ^ (1/3)) / (6 (9 i √ (16303) + 8111) ^ (1/3)) + 16/3 or x = 1/3 (10 - 3 √ (11)) ^ (-1/3) ((-1) ^ (1/3) (10 - 3 √ (11)) ^ (2/3) - (-1) ^ (2/3)) - 1/3 or x = 1/3 ((-10 - 3 √ (11)) ^ (1/3) - (-1) ^ (1/3) (3 √ (11) - 10) ^ (1/3)) - 1/3 or x = 1/3 (10 - 3 √ (11)) ^ (-1/3) ( - (10 - 3 √ (11)) ^ (2/3) - 1) - 1/3

3. x = 2/5 or x = (i √ (3)) / 2 - 1/2 or x = - (i √ (3)) / 2 - 1/2

4. x = 1/4 + (4 √ (54714) + 441) ^ (1/3) / (4 3^ (2/3)) - 61 / (4 (12 √ (54714) + 1323) ^ (1/3)) or x = ( - (-3) ^ (1/3) (4 √ (54714) + 441) ^ (2/3) - 61 (-3) ^ (2/3)) / (12 (4 √ (54714) + 441) ^ (1/3)) + 1/4 or x = (61 (-3 / (441 + 4 √ (54714))) ^ (1/3) + (-1) ^ (2/3) (441 + 4 √ (54714)) ^ (1/3)) / (4 3^ (2/3)) + 1/4

Step-by-step explanation:

Too long! I try to add to the comments!