# Solve for t (4(t-1))/8=(2(t+3))/8 4(t-1)8=2(t+3)8
Factor each term.
Reduce the expression 4(t-1)8 by cancelling the common factors.
Factor 4 out of 8.
4(t-1)4⋅2=2(t+3)8
Cancel the common factor.
4(t-1)4⋅2=2(t+3)8
Rewrite the expression.
t-12=2(t+3)8
t-12=2(t+3)8
Reduce the expression 2(t+3)8 by cancelling the common factors.
Factor 2 out of 8.
t-12=2(t+3)2⋅4
Cancel the common factor.
t-12=2(t+3)2⋅4
Rewrite the expression.
t-12=t+34
t-12=t+34
t-12=t+34
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. The t-12 expression needs to be multiplied by 22 to make the denominator 4.
t-12⋅22=t+34
Multiply the expression by a factor of 1 to create the least common denominator (LCD) of 4.
(t-1)(2)
Simplify.
Apply the distributive property.
t⋅2-1⋅24=t+34
Simplify the expression.
Move 2 to the left of t.
2⋅t-1⋅24=t+34
Multiply -1 by 2.
2t-24=t+34
2t-24=t+34
2t-24=t+34
2t-24=t+34
Since the expression on each side of the equation has the same denominator, the numerators must be equal.
2t-2=t+3
Move all terms containing t to the left side of the equation.
Subtract t from both sides of the equation.
2t-2-t=3
Subtract t from 2t.
t-2=3
t-2=3
Move all terms not containing t to the right side of the equation.
Add 2 to both sides of the equation.
t=3+2
Add 3 and 2.
t=5
t=5
Solve for t (4(t-1))/8=(2(t+3))/8

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