Question

Solve for `x` in `(a+b-x)/c+(a+c-x)/b+(c+b-x)/a+(4x)/(a+b+c)=1`?

Answer 1

`(a+b-x)/c+(a+c-x)/b+(c+b-x)/a+(4x)/(a+b+c)=1`

`=>(a+b-x)/c+1+(a+c-x)/b+1+(c+b-x)/a+1+(4x)/(a+b+c)-3-1=0`
`=>(a+b+c-x)/c+(a+c+b-x)/b+(c+b+a-x)/a-4(1-x/(a+b+c))=0`

`=>(a+b+c-x)(1/c+1/b+1/a)-4((a+b+c-x)/(a+b+c))=0`

`=>(a+b+c-x)(1/c+1/b+1/a-4/(a+b+c))=0`

So

`=>(a+b+c-x)=0`

For `(1/c+1/b+1/a-4/(a+b+c))!=0`

Hence `x=a+b+c`