Solve 16/g=x+42/x

$$\frac { 16 } { g } = \frac { x + 42 } { x }$$

Solve for g

$$g=\frac{16x}{x+42}$$

$$x\neq 0\text{ and }x\neq -42$$

Steps for Solving Linear Equation

Variable g cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by gx, the least common multiple of g,x.

$$x\times 16=g\left(x+42\right)$$

Use the distributive property to multiply g by x+42.

$$x\times 16=gx+42g$$

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

$$gx+42g=x\times 16$$

Combine all terms containing g.

$$\left(x+42\right)g=x\times 16$$

The equation is in standard form.

$$\left(x+42\right)g=16x$$

Divide both sides by x+42.

$$\frac{\left(x+42\right)g}{x+42}=\frac{16x}{x+42}$$

Dividing by x+42 undoes the multiplication by x+42.

$$g=\frac{16x}{x+42}$$

Variable g cannot be equal to 0.

$$g=\frac{16x}{x+42}\text{, }g\neq 0$$

Solve for x

$$x=\frac{42g}{16-g}$$

$$g\neq 0\text{ and }g\neq 16$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by gx, the least common multiple of g,x.

$$x\times 16=g\left(x+42\right)$$

Use the distributive property to multiply g by x+42.

$$x\times 16=gx+42g$$

Subtract gx from both sides.

$$x\times 16-gx=42g$$

Combine all terms containing x.

$$\left(16-g\right)x=42g$$

Divide both sides by 16-g.

$$\frac{\left(16-g\right)x}{16-g}=\frac{42g}{16-g}$$

Dividing by 16-g undoes the multiplication by 16-g.

$$x=\frac{42g}{16-g}$$

Variable x cannot be equal to 0.

$$x=\frac{42g}{16-g}\text{, }x\neq 0$$