Solve 5x(x-1)=h(x^2-1)

$$5 x ( x - 1 ) = h ( x ^ { 2 } - 1 )$$

Solve for h (complex solution)

$$\left\{\begin{matrix}h=\frac{5x}{x+1}\text{, }&x\neq -1\\h\in \mathrm{C}\text{, }&x=1\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 5x by x-1.

$$5x^{2}-5x=h\left(x^{2}-1\right)$$

Use the distributive property to multiply h by x^{2}-1.

$$5x^{2}-5x=hx^{2}-h$$

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

$$hx^{2}-h=5x^{2}-5x$$

Combine all terms containing h.

$$\left(x^{2}-1\right)h=5x^{2}-5x$$

Divide both sides by x^{2}-1.

$$\frac{\left(x^{2}-1\right)h}{x^{2}-1}=\frac{5x\left(x-1\right)}{x^{2}-1}$$

Dividing by x^{2}-1 undoes the multiplication by x^{2}-1.

$$h=\frac{5x\left(x-1\right)}{x^{2}-1}$$

Divide 5x\left(-1+x\right) by x^{2}-1.

$$h=\frac{5x}{x+1}$$

Solve for h

$$\left\{\begin{matrix}h=\frac{5x}{x+1}\text{, }&x\neq -1\\h\in \mathrm{R}\text{, }&x=1\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 5x by x-1.

$$5x^{2}-5x=h\left(x^{2}-1\right)$$

Use the distributive property to multiply h by x^{2}-1.

$$5x^{2}-5x=hx^{2}-h$$

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

$$hx^{2}-h=5x^{2}-5x$$

Combine all terms containing h.

$$\left(x^{2}-1\right)h=5x^{2}-5x$$

Divide both sides by x^{2}-1.

$$\frac{\left(x^{2}-1\right)h}{x^{2}-1}=\frac{5x\left(x-1\right)}{x^{2}-1}$$

Dividing by x^{2}-1 undoes the multiplication by x^{2}-1.

$$h=\frac{5x\left(x-1\right)}{x^{2}-1}$$

Divide 5x\left(-1+x\right) by x^{2}-1.

$$h=\frac{5x}{x+1}$$

Solve for x

$$\left\{\begin{matrix}\\x=1\text{, }&\text{unconditionally}\\x=\frac{h}{5-h}\text{, }&h\neq 5\end{matrix}\right.$$