# Solve for z z/2-z/3=54 z2-z3=54
Simplify z2-z3.
To write z2 as a fraction with a common denominator, multiply by 33.
z2⋅33-z3=54
To write -z3 as a fraction with a common denominator, multiply by 22.
z2⋅33-z3⋅22=54
Write each expression with a common denominator of 6, by multiplying each by an appropriate factor of 1.
Multiply z2 and 33.
z⋅32⋅3-z3⋅22=54
Multiply 2 by 3.
z⋅36-z3⋅22=54
Multiply z3 and 22.
z⋅36-z⋅23⋅2=54
Multiply 3 by 2.
z⋅36-z⋅26=54
z⋅36-z⋅26=54
Combine the numerators over the common denominator.
z⋅3-z⋅26=54
Simplify the numerator.
Factor z out of z⋅3-z⋅2.
Factor z out of z⋅3.
z(3)-z⋅26=54
Factor z out of -z⋅2.
z(3)+z(-1⋅2)6=54
Factor z out of z(3)+z(-1⋅2).
z(3-1⋅2)6=54
z(3-1⋅2)6=54
Multiply -1 by 2.
z(3-2)6=54
Subtract 2 from 3.
z⋅16=54
z⋅16=54
Multiply z by 1.
z6=54
z6=54
Multiply both sides of the equation by 6.
6⋅z6=6⋅54
Simplify both sides of the equation.
Cancel the common factor of 6.
Cancel the common factor.
6⋅z6=6⋅54
Rewrite the expression.
z=6⋅54
z=6⋅54
Multiply 6 by 54.
z=324
z=324
Solve for z z/2-z/3=54

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