How do you solve #\frac { 2} { t } - 1= 5- \frac { 1} { t }#?

3 Answers
David Drayer · EZ as pi
Mar 9, 2017

isolate the variable #t# by removing the variable from the denominator and then solve for #t# using the inverse order of operations giving
#t=1/2#

Explanation:

The inverse order of operation is PE SADM Remember this as if you find you have lost your cell phone in PE class you are a SAD Man.

The # _ # acts as parenthesis so the first step is to remove the division by multiplying everything by t

# t { 2/t -1 = 5 - 1/t} # This gives

# 2 -1 t = 5t - 1# Now add 1 to both sides of the equation

# 2 + 1 - 1 t = 5 t -1 + 1# This gives

# 3 -1 t = 5 t # combine the variable by adding 1 t to both sides.

# 3 - 1 t + 1 t = 5t + 1t # This gives

# 3 = 6 t # Divide both sides by 6

# 3/6 = (6t)/6# simplifying gives

# 1/2 = t#

EZ as pi
Mar 10, 2017

#t = 1/2#

Explanation:

Re-arrange the equation first to get:

#2/t +1/t =5+1#

Collecting like terms gives:

#3/t = 6#

Make a fraction on both sides:

#3/t = 6/1#

Invert both sides

#t/3 = 1/6" "larr xx 3#

#t = 3/6 = 1/2#

Barney V.
Mar 10, 2017

#t=1/2#

Explanation:

#2/t-1=5-1/t#

multiply L.H.S and R.H.S. by# t/1#

#:.2/cancelt^color(red)1*cancelt^color(red)1/1-1/1*t/1=5/1*t/1-1/cancelt^color(red)1*cancelt^color(red)1/1#

#:.2-t=5t-1#

#:.-t-5t=-1-2#

#:.-6t=-3#

multiply L.H.S and R.H.S. by# -1#

#:.6t=3#

#:.t=3/6#

#:.color(red)(t=1/2#

substitute #color(red)(t=1/2#

#2/color(red)(1/2)-1=5-1/color(red)(1/2#

#:.4-1=5-2#

#:.3=3#

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