Question

Question #85911

Answer 1

If `w=i-2`
`color(white)("XXXX")1/(5-w) = (7+i)/50`

Explanation:

`1/(5-w)`
`color(white)("XXXX")=1/(5-(i-2))`

`color(white)("XXXX")=1/(7-i)`

To rationalize the denominator, multiply both the numerator and denominator by the conjugate of the denominator
`color(white)("XXXX")=1/(7-i) * (7+i)/(7+i)`

`color(white)("XXXX")= (7+i)/(7^2-i^2) = (7+i)/(49-(-1)) = (7+i)/50`