1n+34=1112

Subtract 34 from both sides of the equation.

1n=1112-34

To write -34 as a fraction with a common denominator, multiply by 33.

1n=1112-34⋅33

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

Multiply 34 and 33.

1n=1112-3⋅34⋅3

Multiply 4 by 3.

1n=1112-3⋅312

1n=1112-3⋅312

Combine the numerators over the common denominator.

1n=11-3⋅312

Simplify the numerator.

Multiply -3 by 3.

1n=11-912

Subtract 9 from 11.

1n=212

1n=212

Cancel the common factor of 2 and 12.

Factor 2 out of 2.

1n=2(1)12

Cancel the common factors.

Factor 2 out of 12.

1n=2⋅12⋅6

Cancel the common factor.

1n=2⋅12⋅6

Rewrite the expression.

1n=16

1n=16

1n=16

1n=16

Multiply each term by a factor of 1 that will equate all the denominators. In this case, all terms need a denominator of 6n. The 1n expression needs to be multiplied by 66 to make the denominator 6n. The 16 expression needs to be multiplied by nn to make the denominator 6n.

1n⋅66=16⋅nn

Multiply the expression by a factor of 1 to create the least common denominator (LCD) of 6n.

1(6)

Multiply 6 by 1.

66n=16⋅nn

Multiply the expression by a factor of 1 to create the least common denominator (LCD) of 6n.

1(n)

Multiply n by 1.

66n=n6n

66n=n6n

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

6=n

Rewrite the equation as n=6.

n=6

Solve for n 1/n+3/4=11/12