5/(4-√11) + 1/(3+√7) - 6/(√7-2) - (√7-5)/2 = 4+√11-3√7

To simplify the left side of the equation, we need to rationalize the denominators.

Starting with the first term: 5/(4-√11)
To rationalize the denominator, we multiply the numerator and denominator by the conjugate of the denominator, which is (4+√11):
5/(4-√11) * (4+√11)/(4+√11)
= (5(4+√11))/(16-11)
= (20+5√11)/5
= 4+√11

Moving on to the second term: 1/(3+√7)
To rationalize the denominator, we multiply the numerator and denominator by the conjugate of the denominator, which is (3-√7):
1/(3+√7) * (3-√7)/(3-√7)
= (1(3-√7))/(9-7)
= (3-√7)/2

Next, the third term: 6/(√7-2)
To rationalize the denominator, we multiply the numerator and denominator by the conjugate of the denominator, which is (√7+2):
6/(√7-2) * (√7+2)/(√7+2)
= (6(√7+2))/(7-4)
= (6√7+12)/3
= 2√7+4

Finally, the fourth term: (√7-5)/2
This term is already simplified.

Putting it all together, the left side of the equation simplifies to:
4+√11 + (3-√7)/2 - (2√7+4) - (√7-5)/2

Combining like terms:
= 4 + (3-√7 - 2√7 - √7)/2 + (5-4)/2
= 4 + (3-3√7)/2 + 1/2
= 4 + (3-3√7 + 1)/2
= 4 + (4-3√7)/2
= (8+4-3√7)/2
= (12-3√7)/2
= 6 - (3/2)√7

So, the left side of the equation simplifies to 6 - (3/2)√7, which is not equal to 4+√11-3√7.