3y4+y-23=2y+12-1

To write 3y4 as a fraction with a common denominator, multiply by 33.

3y4⋅33+y-23=2y+12-1

To write y-23 as a fraction with a common denominator, multiply by 44.

3y4⋅33+y-23⋅44=2y+12-1

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

Multiply 3y4 and 33.

3y⋅34⋅3+y-23⋅44=2y+12-1

Multiply 4 by 3.

3y⋅312+y-23⋅44=2y+12-1

Multiply y-23 and 44.

3y⋅312+(y-2)⋅43⋅4=2y+12-1

Multiply 3 by 4.

3y⋅312+(y-2)⋅412=2y+12-1

3y⋅312+(y-2)⋅412=2y+12-1

Combine the numerators over the common denominator.

3y⋅3+(y-2)⋅412=2y+12-1

Simplify the numerator.

Multiply 3 by 3.

9y+(y-2)⋅412=2y+12-1

Apply the distributive property.

9y+y⋅4-2⋅412=2y+12-1

Move 4 to the left of y.

9y+4⋅y-2⋅412=2y+12-1

Multiply -2 by 4.

9y+4⋅y-812=2y+12-1

Add 9y and 4y.

13y-812=2y+12-1

13y-812=2y+12-1

13y-812=2y+12-1

To write -1 as a fraction with a common denominator, multiply by 22.

13y-812=2y+12-1⋅22

Simplify terms.

Combine -1 and 22.

13y-812=2y+12+-1⋅22

Combine the numerators over the common denominator.

13y-812=2y+1-1⋅22

13y-812=2y+1-1⋅22

Simplify the numerator.

Multiply -1 by 2.

13y-812=2y+1-22

Subtract 2 from 1.

13y-812=2y-12

13y-812=2y-12

13y-812=2y-12

Subtract 2y-12 from both sides of the equation.

13y-812-2y-12=0

To write -2y-12 as a fraction with a common denominator, multiply by 66.

13y-812-2y-12⋅66=0

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

Multiply 2y-12 and 66.

13y-812-(2y-1)⋅62⋅6=0

Multiply 2 by 6.

13y-812-(2y-1)⋅612=0

13y-812-(2y-1)⋅612=0

Combine the numerators over the common denominator.

13y-8-(2y-1)⋅612=0

Simplify the numerator.

Apply the distributive property.

13y-8+(-(2y)–1)⋅612=0

Multiply 2 by -1.

13y-8+(-2y–1)⋅612=0

Multiply -1 by -1.

13y-8+(-2y+1)⋅612=0

Apply the distributive property.

13y-8-2y⋅6+1⋅612=0

Multiply 6 by -2.

13y-8-12y+1⋅612=0

Multiply 6 by 1.

13y-8-12y+612=0

Subtract 12y from 13y.

y-8+612=0

Add -8 and 6.

y-212=0

y-212=0

y-212=0

Multiply both sides of the equation by 12.

12⋅y-212=12⋅0

Cancel the common factor of 12.

Cancel the common factor.

12⋅y-212=12⋅0

Rewrite the expression.

y-2=12⋅0

y-2=12⋅0

Multiply 12 by 0.

y-2=0

y-2=0

Add 2 to both sides of the equation.

y=2

Solve for y (3y)/4+(y-2)/3=(2y+1)/2-1