12+2z+1=34

Subtract 12 from both sides of the equation.

2z+1=34-12

To write -12 as a fraction with a common denominator, multiply by 22.

2z+1=34-12⋅22

Write each expression with a common denominator of 4, by multiplying each by an appropriate factor of 1.

Multiply 12 and 22.

2z+1=34-22⋅2

Multiply 2 by 2.

2z+1=34-24

2z+1=34-24

Combine the numerators over the common denominator.

2z+1=3-24

Subtract 2 from 3.

2z+1=14

2z+1=14

Multiply each term by a factor of 1 that will equate all the denominators. In this case, all terms need a denominator of 4(z+1). The 2z+1 expression needs to be multiplied by 44 to make the denominator 4(z+1). The 14 expression needs to be multiplied by z+1z+1 to make the denominator 4(z+1).

2z+1⋅44=14⋅z+1z+1

Multiply the expression by a factor of 1 to create the least common denominator (LCD) of 4(z+1).

2(4)

Multiply 2 by 4.

84(z+1)=14⋅z+1z+1

Multiply the expression by a factor of 1 to create the least common denominator (LCD) of 4(z+1).

1(z+1)

Multiply z+1 by 1.

84(z+1)=z+14(z+1)

84(z+1)=z+14(z+1)

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

8=z+1

Rewrite the equation as z+1=8.

z+1=8

Subtract 1 from both sides of the equation.

z=8-1

Subtract 1 from 8.

z=7

z=7

Solve for z 1/2+2/(z+1)=3/4