Solve 2^2++1=2x+1/t+1

$$2 ^ { 2 + + 1 } = \frac { 2 x + 1 } { t + 1 }$$

Solve for t

$$t=\frac{x}{4}-\frac{7}{8}$$

$$x\neq -\frac{1}{2}$$

Steps for Solving Linear Equation

Variable t cannot be equal to -1 since division by zero is not defined. Multiply both sides of the equation by t+1.

$$\left(t+1\right)\times 2^{2+1}=2x+1$$

Add 2 and 1 to get 3.

$$\left(t+1\right)\times 2^{3}=2x+1$$

Calculate 2 to the power of 3 and get 8.

$$\left(t+1\right)\times 8=2x+1$$

Use the distributive property to multiply t+1 by 8.

$$8t+8=2x+1$$

Subtract 8 from both sides.

$$8t=2x+1-8$$

Subtract 8 from 1 to get -7.

$$8t=2x-7$$

Divide both sides by 8.

$$\frac{8t}{8}=\frac{2x-7}{8}$$

Dividing by 8 undoes the multiplication by 8.

$$t=\frac{2x-7}{8}$$

Divide 2x-7 by 8.

$$t=\frac{x}{4}-\frac{7}{8}$$

Variable t cannot be equal to -1.

$$t=\frac{x}{4}-\frac{7}{8}\text{, }t\neq -1$$

Solve for x

$$x=4t+\frac{7}{2}$$

$$t\neq -1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by t+1.

$$\left(t+1\right)\times 2^{2+1}=2x+1$$

Add 2 and 1 to get 3.

$$\left(t+1\right)\times 2^{3}=2x+1$$

Calculate 2 to the power of 3 and get 8.

$$\left(t+1\right)\times 8=2x+1$$

Use the distributive property to multiply t+1 by 8.

$$8t+8=2x+1$$

Swap sides so that all variable terms are on the left hand side.

$$2x+1=8t+8$$

Subtract 1 from both sides.

$$2x=8t+8-1$$

Subtract 1 from 8 to get 7.

$$2x=8t+7$$

Divide both sides by 2.

$$\frac{2x}{2}=\frac{8t+7}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$x=\frac{8t+7}{2}$$

Divide 8t+7 by 2.

$$x=4t+\frac{7}{2}$$