Solve (f+g)(x)=4/x+5

$$( f + g ) ( x ) = \frac { 4 } { x } + 5$$

Solve for f

$$f=-g+\frac{5}{x}+\frac{4}{x^{2}}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x.

$$\left(f+g\right)xx=4+x\times 5$$

Multiply x and x to get x^{2}.

$$\left(f+g\right)x^{2}=4+x\times 5$$

Use the distributive property to multiply f+g by x^{2}.

$$fx^{2}+gx^{2}=4+x\times 5$$

Subtract gx^{2} from both sides.

$$fx^{2}=4+x\times 5-gx^{2}$$

Reorder the terms.

$$fx^{2}=-gx^{2}+5x+4$$

The equation is in standard form.

$$x^{2}f=4+5x-gx^{2}$$

Divide both sides by x^{2}.

$$\frac{x^{2}f}{x^{2}}=\frac{4+5x-gx^{2}}{x^{2}}$$

Dividing by x^{2} undoes the multiplication by x^{2}.

$$f=\frac{4+5x-gx^{2}}{x^{2}}$$

Divide -gx^{2}+5x+4 by x^{2}.

$$f=-g+\frac{5x+4}{x^{2}}$$

Solve for g

$$g=-f+\frac{5}{x}+\frac{4}{x^{2}}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x.

$$\left(f+g\right)xx=4+x\times 5$$

Multiply x and x to get x^{2}.

$$\left(f+g\right)x^{2}=4+x\times 5$$

Use the distributive property to multiply f+g by x^{2}.

$$fx^{2}+gx^{2}=4+x\times 5$$

Subtract fx^{2} from both sides.

$$gx^{2}=4+x\times 5-fx^{2}$$

Reorder the terms.

$$gx^{2}=-fx^{2}+5x+4$$

The equation is in standard form.

$$x^{2}g=4+5x-fx^{2}$$

Divide both sides by x^{2}.

$$\frac{x^{2}g}{x^{2}}=\frac{4+5x-fx^{2}}{x^{2}}$$

Dividing by x^{2} undoes the multiplication by x^{2}.

$$g=\frac{4+5x-fx^{2}}{x^{2}}$$

Divide -fx^{2}+5x+4 by x^{2}.

$$g=-f+\frac{5x+4}{x^{2}}$$