Question #85911

1 Answer
Alan P. · Jim H · dani83
Aug 24, 2015

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#

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