Solve p(x)divx+1p(x)=x100-56x^34+6divx+1

$$p ( x ) \div x + 1 p ( x ) = x 100 - 56 x ^ { 34 } + 6 \div x + 1$$

Solve for p

$$\left\{\begin{matrix}p=-\frac{56x^{35}-xx_{100}-x-6}{x\left(x+1\right)}\text{, }&x\neq -1\text{ and }x\neq 0\\p\in \mathrm{R}\text{, }&x=-1\text{ and }x_{100}=61\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x.

$$px+1pxx=xx_{100}-56x^{34}x+6+x$$

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

$$px+1px^{2}=xx_{100}-56x^{34}x+6+x$$

To multiply powers of the same base, add their exponents. Add 34 and 1 to get 35.

$$px+1px^{2}=xx_{100}-56x^{35}+6+x$$

Reorder the terms.

$$px^{2}+px=-56x^{35}+xx_{100}+x+6$$

Combine all terms containing p.

$$\left(x^{2}+x\right)p=-56x^{35}+xx_{100}+x+6$$

The equation is in standard form.

$$\left(x^{2}+x\right)p=6+x+xx_{100}-56x^{35}$$

Divide both sides by x+x^{2}.

$$\frac{\left(x^{2}+x\right)p}{x^{2}+x}=\frac{6+x+xx_{100}-56x^{35}}{x^{2}+x}$$

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

$$p=\frac{6+x+xx_{100}-56x^{35}}{x^{2}+x}$$

Divide -56x^{35}+xx_{100}+x+6 by x+x^{2}.

$$p=\frac{6+x+xx_{100}-56x^{35}}{x\left(x+1\right)}$$