How do you solve #\frac { 1 } { 4 } + \frac { 1 } { 5 } = \frac { 1 } { t }#?

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Answer 1 · 2018-07-20T00:50:41

Multiply all three terms by # 4 xx 5 xx t# to remove the denominators and then solve by working backwards.

# ( 4 xx 5 xx t ) xx 1/4 + ( 4 xx 5 xx t) xx 1/5 = (4 xx 5 xx t) xx 1/t#

This gives

# 5 xx t + 4 xx t = 4xx 5#

Combining like terms gives

# 9t = 20#

Divide both sides by 9

# 9t/9 = 20/9 #

# t = 20/9 = 2 2/9#