2+13t=1+14t

Combine 13 and t.

2+t3=1+14t

Combine 14 and t.

2+t3=1+t4

Subtract t4 from both sides of the equation.

2+t3-t4=1

To write t3 as a fraction with a common denominator, multiply by 44.

2+t3⋅44-t4=1

To write -t4 as a fraction with a common denominator, multiply by 33.

2+t3⋅44-t4⋅33=1

Write each expression with a common denominator of 12, by multiplying each by an appropriate factor of 1.

Multiply t3 and 44.

2+t⋅43⋅4-t4⋅33=1

Multiply 3 by 4.

2+t⋅412-t4⋅33=1

Multiply t4 and 33.

2+t⋅412-t⋅34⋅3=1

Multiply 4 by 3.

2+t⋅412-t⋅312=1

2+t⋅412-t⋅312=1

Combine the numerators over the common denominator.

2+t⋅4-t⋅312=1

Simplify each term.

Simplify the numerator.

Factor t out of t⋅4-t⋅3.

Factor t out of t⋅4.

2+t(4)-t⋅312=1

Factor t out of -t⋅3.

2+t(4)+t(-1⋅3)12=1

Factor t out of t(4)+t(-1⋅3).

2+t(4-1⋅3)12=1

2+t(4-1⋅3)12=1

Multiply -1 by 3.

2+t(4-3)12=1

Subtract 3 from 4.

2+t⋅112=1

2+t⋅112=1

Multiply t by 1.

2+t12=1

2+t12=1

2+t12=1

Subtract 2 from both sides of the equation.

t12=1-2

Subtract 2 from 1.

t12=-1

t12=-1

Multiply both sides of the equation by 12.

12⋅t12=12⋅-1

Cancel the common factor of 12.

Cancel the common factor.

12⋅t12=12⋅-1

Rewrite the expression.

t=12⋅-1

t=12⋅-1

Multiply 12 by -1.

t=-12

t=-12

Solve for t 2+1/3t=1+1/4t