1. 1/(x + 4) + 1/(x – 6) = 0

Here Numerator of two fractions are same = 1, 

So According to formula : 

x + 4 + x- 6 = 0 

⇒ 2x – 2 = 0 

⇒ 2x = 

⇒ x = 1

2. 5/(3x + 2) + 5/(2x + 8) = 0

Here, Numerator of two fractions are same = 5, 

So according to formula : 

3x + 2 + 2x + 8 = 0 

⇒ 3x + 2x + 2 + 8 = 0 

⇒ 5x + 10 = 0 

⇒ 5x = -10 

⇒ x = -2

3. (2x + 4)/(2x + 1) = (2x + 1)/(2x + 4)

Sum of numerators of both sides

= 2x + 4 + 2x + 1 = 4x + 5

Sum of denominators in both sides

= 2x + 1 + 2x + 4 = 4x + 5 

Two sums are equal, so by the formula 4x + 5 = 0

⇒ 4x = -5

⇒ x = -5/4

4. (3x + 2)/(5x + 7) = (x + 1)/(3x – 1)

Sum of numerators of two sides 

= 3x + 2 + x + 1 = 4x + 3 …..(i) 

Sum of denominators of two sides 

= 5x + 7 + 3x – 1 = 8x + 6 …(ii) 

Ratio of (i) and (ii) is 1 : 2.

So, by formula, equation any sum equal to zero, 

4x + 3 = 0 

⇒ 4x = – 3 

⇒ x = – 3/4