Solve 2t+3/3t+1-t+5/3t+1=1/4

$$\frac { 2 t + 3 } { 3 t + 1 } - \frac { t + 5 } { 3 t + 1 } = \frac { 1 } { 4 }$$

Solve for t

$$t=9$$

Steps for Solving Linear Equation

Variable t cannot be equal to -\frac{1}{3} since division by zero is not defined. Multiply both sides of the equation by 4\left(3t+1\right), the least common multiple of 3t+1,4.

$$4\left(2t+3\right)-4\left(t+5\right)=3t+1$$

Use the distributive property to multiply 4 by 2t+3.

$$8t+12-4\left(t+5\right)=3t+1$$

Use the distributive property to multiply -4 by t+5.

$$8t+12-4t-20=3t+1$$

Combine 8t and -4t to get 4t.

$$4t+12-20=3t+1$$

Subtract 20 from 12 to get -8.

$$4t-8=3t+1$$

Subtract 3t from both sides.

$$4t-8-3t=1$$

Combine 4t and -3t to get t.

$$t-8=1$$

Add 8 to both sides.

$$t=1+8$$

Add 1 and 8 to get 9.

$$t=9$$