How do you solve #\frac { 1} { z } + \frac { 12} { 2z } = 1#?

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Answer 1 · 2016-12-09T11:51:55

See explanation.

First we have to find the domain of the equation. Since #x# appears in the denominator the expressions with it cannot be zero:

#z !=0# and #2x!=0 => z!=0#.

Finally the domain is #z in RR-{0}#

Now we can solve the equation:

#1/z+12/(2z)=1#

#1/z+6/z=1#

#7/z=1#

#z=7#

Number #7# is different from zero, so it lies within the domain, so we can write the answer:

The equation has a solution #z=7#