Solve H/k+3*(k-1)=2

$$\frac { H } { k + 3 } \times ( k - 1 ) = 2$$

Solve for H

$$H=\frac{2\left(k+3\right)}{k-1}$$

$$k\neq -3\text{ and }k\neq 1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by k+3.

$$H\left(k-1\right)=2\left(k+3\right)$$

Use the distributive property to multiply H by k-1.

$$Hk-H=2\left(k+3\right)$$

Use the distributive property to multiply 2 by k+3.

$$Hk-H=2k+6$$

Combine all terms containing H.

$$\left(k-1\right)H=2k+6$$

Divide both sides by k-1.

$$\frac{\left(k-1\right)H}{k-1}=\frac{2k+6}{k-1}$$

Dividing by k-1 undoes the multiplication by k-1.

$$H=\frac{2k+6}{k-1}$$

Divide 6+2k by k-1.

$$H=\frac{2\left(k+3\right)}{k-1}$$

Solve for k

$$k=\frac{H+6}{H-2}$$

$$H\neq 0\text{ and }H\neq 2$$

Steps for Solving Linear Equation

Variable k cannot be equal to -3 since division by zero is not defined. Multiply both sides of the equation by k+3.

$$H\left(k-1\right)=2\left(k+3\right)$$

Use the distributive property to multiply H by k-1.

$$Hk-H=2\left(k+3\right)$$

Use the distributive property to multiply 2 by k+3.

$$Hk-H=2k+6$$

Subtract 2k from both sides.

$$Hk-H-2k=6$$

Add H to both sides.

$$Hk-2k=6+H$$

Combine all terms containing k.

$$\left(H-2\right)k=6+H$$

The equation is in standard form.

$$\left(H-2\right)k=H+6$$

Divide both sides by H-2.

$$\frac{\left(H-2\right)k}{H-2}=\frac{H+6}{H-2}$$

Dividing by H-2 undoes the multiplication by H-2.

$$k=\frac{H+6}{H-2}$$

Variable k cannot be equal to -3.

$$k=\frac{H+6}{H-2}\text{, }k\neq -3$$