If `(sqrt(7)-1)/(sqrt(7)+1)-(sqrt(7)+1)/(sqrt(7)-1)=a+sqrt(7)b` then the value of a and b are respectively

Options

A. `sqrt(7),-1`
B. `sqrt(7),1`
C. `0,-(2)/(3)`
D. `-(2)/(3),0`

Answer

To solve the equation

\[ \frac{\sqrt{7}-1}{\sqrt{7}+1} - \frac{\sqrt{7}+1}{\sqrt{7}-1} = a + \sqrt{7}b, \]

we will follow these steps:

### Step 1: Combine the fractions
To combine the two fractions, we need a common denominator. The common denominator is \((\sqrt{7}+1)(\sqrt{7}-1)\). Thus, we rewrite the equation:

\[ \frac{(\sqrt{7}-1)^2 - (\sqrt{7}+1)^2}{(\sqrt{7}+1)(\sqrt{7}-1)}. \]