Type a math problem

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Type a math problem

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.

${h=yx ,h =0, x =0andy =0y=0andx=0 $

Steps for Solving Linear Equation

y = h ^ { - 1 } ( x )

$y=h_{−1}(x)$

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

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

h^{\left(-1\right)}x=y

$h_{(−1)}x=y$

Reorder the terms.

Reorder the terms.

\frac{1}{h}x=y

$h1 x=y$

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

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

1x=yh

$1x=yh$

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

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

yh=1x

$yh=1x$

Reorder the terms.

Reorder the terms.

hy=x

$hy=x$

The equation is in standard form.

The equation is in standard form.

yh=x

$yh=x$

Divide both sides by y.

Divide both sides by $y$.

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

$yyh =yx $

Dividing by y undoes the multiplication by y.

Dividing by $y$ undoes the multiplication by $y$.

h=\frac{x}{y}

$h=yx $

Variable h cannot be equal to 0.

Variable $h$ cannot be equal to $0$.

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

$h=yx ,h =0$

Solve for x

x=hy,h\neq 0

$x=hy,h =0$

Solution Steps

y = h ^ { - 1 } ( x )

$y=h_{−1}(x)$

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

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

h^{\left(-1\right)}x=y

$h_{(−1)}x=y$

Reorder the terms.

Reorder the terms.

\frac{1}{h}x=y

$h1 x=y$

Multiply both sides of the equation by h.

Multiply both sides of the equation by $h$.

1x=yh

$1x=yh$

Reorder the terms.

Reorder the terms.

x=hy

$x=hy$

Solve for y

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

$y=hx ,h =0$

Assign y

y≔\frac{x}{h}

$y:=hx $

Graph

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h^{\left(-1\right)}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^{\left(-1\right)}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.

Examples

Quadratic equation

{ x } ^ { 2 } - 4 x - 5 = 0

$x_{2}−4x−5=0$

Trigonometry

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

$4sinθcosθ=2sinθ$

Linear equation

y = 3x + 4

$y=3x+4$

Arithmetic

699 * 533

$699∗533$

Matrix

\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { - 1 } & { 1 } & { 5 } \end{array} \right]

$[25 34 ][2−1 01 35 ]$

Simultaneous equation

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

${8x+2y=467x+3y=47 $

Differentiation

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

$dxd (x−5)(3x_{2}−2) $

Integration

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

$∫_{0}xe_{−x_{2}}dx$

Limits

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

$x→−3lim x_{2}+2x−3x_{2}−9 $

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