Solve 4/x-4-4/4-x=1/2quadQ

$$\frac { 4 } { x - 4 } - \frac { 4 } { 4 - x } = \frac { 1 } { 2 } \quad Q$$

Solve for Q

$$Q=-\frac{16}{4-x}$$

$$x\neq 4$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2\left(x-4\right), the least common multiple of x-4,4-x,2.

$$2\times 4+2\times 4=\frac{1}{2}Q\times 2\left(x-4\right)$$

Do the multiplications.

$$8+8=\frac{1}{2}Q\times 2\left(x-4\right)$$

Add 8 and 8 to get 16.

$$16=\frac{1}{2}Q\times 2\left(x-4\right)$$

Multiply \frac{1}{2} and 2 to get 1.

$$16=Q\left(x-4\right)$$

Use the distributive property to multiply Q by x-4.

$$16=Qx-4Q$$

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

$$Qx-4Q=16$$

Combine all terms containing Q.

$$\left(x-4\right)Q=16$$

Divide both sides by x-4.

$$\frac{\left(x-4\right)Q}{x-4}=\frac{16}{x-4}$$

Dividing by x-4 undoes the multiplication by x-4.

$$Q=\frac{16}{x-4}$$

Solve for x

$$x=4+\frac{16}{Q}$$

$$Q\neq 0$$

Steps for Solving Linear Equation

Variable x cannot be equal to 4 since division by zero is not defined. Multiply both sides of the equation by 2\left(x-4\right), the least common multiple of x-4,4-x,2.

$$2\times 4+2\times 4=\frac{1}{2}Q\times 2\left(x-4\right)$$

Do the multiplications.

$$8+8=\frac{1}{2}Q\times 2\left(x-4\right)$$

Add 8 and 8 to get 16.

$$16=\frac{1}{2}Q\times 2\left(x-4\right)$$

Multiply \frac{1}{2} and 2 to get 1.

$$16=Q\left(x-4\right)$$

Use the distributive property to multiply Q by x-4.

$$16=Qx-4Q$$

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

$$Qx-4Q=16$$

Add 4Q to both sides.

$$Qx=16+4Q$$

The equation is in standard form.

$$Qx=4Q+16$$

Divide both sides by Q.

$$\frac{Qx}{Q}=\frac{4Q+16}{Q}$$

Dividing by Q undoes the multiplication by Q.

$$x=\frac{4Q+16}{Q}$$

Divide 16+4Q by Q.

$$x=4+\frac{16}{Q}$$

Variable x cannot be equal to 4.

$$x=4+\frac{16}{Q}\text{, }x\neq 4$$