Linear Algebra Examples

$u s - g e = f h$

Step 1

Add $g e$ to both sides of the equation.

$u s = f h + g e$

Step 2

Divide each term in $u s = f h + g e$ by $s$ and simplify.

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Step 2.1

Divide each term in $u s = f h + g e$ by $s$ .

$\frac{u s}{s} = \frac{f h}{s} + \frac{g e}{s}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $s$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{u s}{s} = \frac{f h}{s} + \frac{g e}{s}$

Step 2.2.1.2

Divide $u$ by $1$ .

$u = \frac{f h}{s} + \frac{g e}{s}$

Step 3

Set the denominator in $\frac{f h}{s}$ equal to $0$ to find where the expression is undefined.

$s = 0$

Step 4

The domain is all values of $f$ that make the expression defined.

Interval Notation:

$(- \infty, 0) \cup (0, \infty)$

Set-Builder Notation:

${f | f \neq 0}$