Solve for h

\left\{\begin{matrix}h=\frac{x}{y}\text{, }&x\neq 0\text{ and }y\neq 0\\h\neq 0\text{, }&y=0\text{ and }x=0\end{matrix}\right.

Solve for x

x=hy,h\neq 0

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h^{-1}x=y

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

\frac{1}{h}x=y

Reorder the terms.

1x=yh

Variable h cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by h.

yh=1x

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

hy=x

Reorder the terms.

yh=x

The equation is in standard form.

\frac{yh}{y}=\frac{x}{y}

Divide both sides by y.

h=\frac{x}{y}

Dividing by y undoes the multiplication by y.

h=\frac{x}{y}\text{, }h\neq 0

Variable h cannot be equal to 0.

h^{-1}x=y

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

\frac{1}{h}x=y

Reorder the terms.

1x=yh

Multiply both sides of the equation by h.

x=hy

Reorder the terms.

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4 \sin \theta \cos \theta = 2 \sin \theta

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y = 3x + 4

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Simultaneous equation

\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.

Differentiation

\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }

Integration

\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x

Limits

\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}