Solve the following equation for `x`:`tan^(-1)(1/4)+2tan^(-1)(1/5)+tan^(-1)(1/6)+tan^(-1)(1/x)=pi/4`

Explanation

`=tan^(-1)(frac{(1/x)+(1/4)}{1- (1/x)xx(1/4)})+tan^(-1)(frac{2 xx(1/5))}{1-(1/5)^2})+tan^(-1)(1/6)= pi/4`

`=tan^(-1)(frac{4+x}{4x-1})+tan^(-1)(5/12)+tan^(-1)(1/6)= pi/4`

`tan^(-1)(frac{4+x}{4x-1})+tan^(-1)(frac{30+12}{72-5})= pi/4`

`frac{67(4+x)+42(4x-1)}{(4x-1)67-42(4+x)}=tan (pi/4)`

`frac{268+67x+168x-42}{268x-67-168-42x}=1`

`277x-268x=-503+42`

`9x=-461`
`x= (-461)/9`