Solve x^3/x+1-p=a/x+1

$$\frac { x ^ { 3 } } { x + 1 } - p = \frac { a } { x + 1 }$$

Solve for a

$$a=x^{3}-px-p$$

$$x\neq -1$$

Solution Steps

Multiply both sides of the equation by x+1.

$$x^{3}-p\left(x+1\right)=a$$

Use the distributive property to multiply -p by x+1.

$$x^{3}-px-p=a$$

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

$$a=x^{3}-px-p$$

Solve for p

$$p=\frac{x^{3}-a}{x+1}$$

$$x\neq -1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x+1.

$$x^{3}-p\left(x+1\right)=a$$

Use the distributive property to multiply -p by x+1.

$$x^{3}-px-p=a$$

Subtract x^{3} from both sides.

$$-px-p=a-x^{3}$$

Combine all terms containing p.

$$\left(-x-1\right)p=a-x^{3}$$

Divide both sides by -x-1.

$$\frac{\left(-x-1\right)p}{-x-1}=\frac{a-x^{3}}{-x-1}$$

Dividing by -x-1 undoes the multiplication by -x-1.

$$p=\frac{a-x^{3}}{-x-1}$$

Divide a-x^{3} by -x-1.

$$p=-\frac{a-x^{3}}{x+1}$$