Question

For equation `1/x + 1/(x - 5) = 3/10`; one value of x is ______.

विकल्प

• `-5/3`

• 10

• –10

• 5

Answer 1

For equation `1/x + 1/(x - 5) = 3/10`; one value of x is 10.

Explanation:

Given equation be,

`1/x + 1/(x - 5) = 3/10`

`\implies (x - 5 + x)/(x(x - 5)) = 3/10`

`\implies (2x - 5)/(x(x - 5)) = 3/10` 

`\implies` 10(2x – 5) = 3x(x – 5)

`\implies` 20x – 50 = 3x² – 15x

`\implies` 3x² – 15x – 20x + 50 = 0

`\implies` 3x² – 35x + 50 = 0

`\implies` 3x² – 30x – 5x + 50 = 0

`\implies` 3x(x – 10) – 5(x – 10) = 0

`\implies` (3x – 5)(x – 10) = 0

Either 3x – 5 = 0 or x – 10 = 0

`\implies` 3x = 5 or x = 10

`\implies` x = `5/3` or 10