Solve 1f(x)+g(x)=(3x^2+2x-8)+(x+2)

$$1 f ( x ) + g ( x ) = ( 3 x ^ { 2 } + 2 x - 8 ) + ( x + 2 )$$

Solve for f

$$f=3x-g+3-\frac{6}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Combine 2x and x to get 3x.

$$1fx+gx=3x^{2}+3x-8+2$$

Add -8 and 2 to get -6.

$$1fx+gx=3x^{2}+3x-6$$

Subtract gx from both sides.

$$1fx=3x^{2}+3x-6-gx$$

Reorder the terms.

$$fx=3x^{2}-gx+3x-6$$

The equation is in standard form.

$$xf=3x^{2}-gx+3x-6$$

Divide both sides by x.

$$\frac{xf}{x}=\frac{3x^{2}-gx+3x-6}{x}$$

Dividing by x undoes the multiplication by x.

$$f=\frac{3x^{2}-gx+3x-6}{x}$$

Divide 3x^{2}-gx+3x-6 by x.

$$f=3x-g+3-\frac{6}{x}$$

Solve for g

$$g=3x-f+3-\frac{6}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Combine 2x and x to get 3x.

$$1fx+gx=3x^{2}+3x-8+2$$

Add -8 and 2 to get -6.

$$1fx+gx=3x^{2}+3x-6$$

Subtract 1fx from both sides.

$$gx=3x^{2}+3x-6-fx$$

The equation is in standard form.

$$xg=3x^{2}-fx+3x-6$$

Divide both sides by x.

$$\frac{xg}{x}=\frac{3x^{2}-fx+3x-6}{x}$$

Dividing by x undoes the multiplication by x.

$$g=\frac{3x^{2}-fx+3x-6}{x}$$

Divide 3x^{2}+3x-6-fx by x.

$$g=3x-f+3-\frac{6}{x}$$