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

12+2z+1=34
Move all terms not containing z to the right side of the equation.
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
Set up the rational expression with the same denominator over the entire equation.
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
Move all terms not containing z to the right side of the equation.
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

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