Solve 8-h/4-k=2h

$$\frac { 8 - h } { 4 - k } = 2 h$$

Solve for h

$$h=-\frac{8}{2k-9}$$

$$k\neq \frac{9}{2}\text{ and }k\neq 4$$

Steps for Solving Linear Equation

Multiply both sides of the equation by -k+4.

$$8-h=2h\left(-k+4\right)$$

Use the distributive property to multiply 2h by -k+4.

$$8-h=-2hk+8h$$

Add 2hk to both sides.

$$8-h+2hk=8h$$

Subtract 8h from both sides.

$$8-h+2hk-8h=0$$

Combine -h and -8h to get -9h.

$$8-9h+2hk=0$$

Subtract 8 from both sides. Anything subtracted from zero gives its negation.

$$-9h+2hk=-8$$

Combine all terms containing h.

$$\left(-9+2k\right)h=-8$$

The equation is in standard form.

$$\left(2k-9\right)h=-8$$

Divide both sides by 2k-9.

$$\frac{\left(2k-9\right)h}{2k-9}=-\frac{8}{2k-9}$$

Dividing by 2k-9 undoes the multiplication by 2k-9.

$$h=-\frac{8}{2k-9}$$

Solve for k

$$k=\frac{9}{2}-\frac{4}{h}$$

$$h\neq 8\text{ and }h\neq 0$$

Steps for Solving Linear Equation

Variable k cannot be equal to 4 since division by zero is not defined. Multiply both sides of the equation by -k+4.

$$8-h=2h\left(-k+4\right)$$

Use the distributive property to multiply 2h by -k+4.

$$8-h=-2hk+8h$$

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

$$-2hk+8h=8-h$$

Subtract 8h from both sides.

$$-2hk=8-h-8h$$

Combine -h and -8h to get -9h.

$$-2hk=8-9h$$

The equation is in standard form.

$$\left(-2h\right)k=8-9h$$

Divide both sides by -2h.

$$\frac{\left(-2h\right)k}{-2h}=\frac{8-9h}{-2h}$$

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

$$k=\frac{8-9h}{-2h}$$

Divide 8-9h by -2h.

$$k=\frac{9}{2}-\frac{4}{h}$$

Variable k cannot be equal to 4.

$$k=\frac{9}{2}-\frac{4}{h}\text{, }k\neq 4$$