Using the sutra Shunyam Samyaschahye, Solve the equation:1. 1/(x + 4)

1.	Using the sutra Shunyam Samyaschahye, Solve the equation:1. 1/(x + 4) + 1/(x - 6) = 02. 5/(3x + 2) + 5/(2x + 8) = 03. (2x + 4)/(2x + 1) = (2x + 1)/(2x + 4)4. (3x + 2)/(5x + 7) = (x + 1)/(3x - 1)
Answer» 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

Using the sutra Shunyam Samyaschahye, Solve the equation:1. 1/(x + 4) + 1/(x - 6) = 02. 5/(3x + 2) + 5/(2x + 8) = 03. (2x + 4)/(2x + 1) = (2x + 1)/(2x + 4)4. (3x + 2)/(5x + 7) = (x + 1)/(3x - 1)

Answer»

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