Solve k-2/H^2k+k-2^7/Hk*2^-1=0

$$\frac { k - 2 } { H ^ { 2 } k } + \frac { k - 2 ^ { 7 } } { H k \cdot 2 ^ { - 1 } } = 0$$

Solve for H

$$H=-\frac{k-2}{2\left(k-128\right)}$$

$$k\neq 2\text{ and }k\neq 128\text{ and }k\neq 0$$

Steps for Solving Linear Equation

Variable H cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by kH^{2}.

$$k-2+2H\left(k-2^{7}\right)=0$$

Calculate 2 to the power of 7 and get 128.

$$k-2+2H\left(k-128\right)=0$$

Use the distributive property to multiply 2H by k-128.

$$k-2+2Hk-256H=0$$

Subtract k from both sides. Anything subtracted from zero gives its negation.

$$-2+2Hk-256H=-k$$

Add 2 to both sides.

$$2Hk-256H=-k+2$$

Combine all terms containing H.

$$\left(2k-256\right)H=-k+2$$

The equation is in standard form.

$$\left(2k-256\right)H=2-k$$

Divide both sides by 2k-256.

$$\frac{\left(2k-256\right)H}{2k-256}=\frac{2-k}{2k-256}$$

Dividing by 2k-256 undoes the multiplication by 2k-256.

$$H=\frac{2-k}{2k-256}$$

Divide -k+2 by 2k-256.

$$H=\frac{2-k}{2\left(k-128\right)}$$

Variable H cannot be equal to 0.

$$H=\frac{2-k}{2\left(k-128\right)}\text{, }H\neq 0$$

Solve for k

$$k=\frac{2\left(128H+1\right)}{2H+1}$$

$$H\neq -\frac{1}{128}\text{ and }H\neq -\frac{1}{2}\text{ and }H\neq 0$$

Steps for Solving Linear Equation

Variable k cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by kH^{2}.

$$k-2+2H\left(k-2^{7}\right)=0$$

Calculate 2 to the power of 7 and get 128.

$$k-2+2H\left(k-128\right)=0$$

Use the distributive property to multiply 2H by k-128.

$$k-2+2Hk-256H=0$$

Add 2 to both sides. Anything plus zero gives itself.

$$k+2Hk-256H=2$$

Add 256H to both sides.

$$k+2Hk=2+256H$$

Combine all terms containing k.

$$\left(1+2H\right)k=2+256H$$

The equation is in standard form.

$$\left(2H+1\right)k=256H+2$$

Divide both sides by 2H+1.

$$\frac{\left(2H+1\right)k}{2H+1}=\frac{256H+2}{2H+1}$$

Dividing by 2H+1 undoes the multiplication by 2H+1.

$$k=\frac{256H+2}{2H+1}$$

Divide 2+256H by 2H+1.

$$k=\frac{2\left(128H+1\right)}{2H+1}$$

Variable k cannot be equal to 0.

$$k=\frac{2\left(128H+1\right)}{2H+1}\text{, }k\neq 0$$