Solve y=h/x^2+kx

$$y = \frac { h } { x ^ { 2 } } + k x$$

Solve for k

$$k=\frac{yx^{2}-h}{x^{3}}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x^{2}.

$$yx^{2}=h+kxx^{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$yx^{2}=h+kx^{3}$$

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

$$h+kx^{3}=yx^{2}$$

Subtract h from both sides.

$$kx^{3}=yx^{2}-h$$

The equation is in standard form.

$$x^{3}k=yx^{2}-h$$

Divide both sides by x^{3}.

$$\frac{x^{3}k}{x^{3}}=\frac{yx^{2}-h}{x^{3}}$$

Dividing by x^{3} undoes the multiplication by x^{3}.

$$k=\frac{yx^{2}-h}{x^{3}}$$

Divide yx^{2}-h by x^{3}.

$$k=\frac{y}{x}-\frac{h}{x^{3}}$$

Solve for h

$$h=-x^{2}\left(kx-y\right)$$

$$x\neq 0$$