How do you solve for #t# in #\frac { 1} { r } = \frac { 1} { t - 6}#?

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Answer 1 · 2018-05-17T11:32:52

#t=r+6#

The biggest problem is that #t# is in the denominator of the fraction.

#1/r =1/(t-6)#

Method 1
Because there is only one term on each side, you can invert the whole fraction:

#r/1 = (t-6)/1#

#r+6=t#

Method 2

Cross multiply to get
#t-6=r#

#t = r+6#

Answer 2 · 2018-05-17T11:38:28

#t=r+6#

Take the reciprocal of both sides:
#1/(1/r)=1/(1/(t-6))#
#r=t-6#

Now add #6# to both sides:
#t-6+6=r+6#
#t=r+6#

Answer 3 · 2018-05-17T11:40:27

#1/r = 1/{t-6}# so cross multiplying #t-6=r# or #t=r+6.#