Linear Algebra Examples

$\frac{t + m f}{m} = g$

Step 1

Multiply both sides by $m$ .

$\frac{t + m f}{m} m = g m$

Step 2

Simplify the left side.

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Step 2.1

Simplify $\frac{t + m f}{m} m$ .

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Step 2.1.1

Cancel the common factor of $m$ .

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Step 2.1.1.1

Cancel the common factor.

$\frac{t + m f}{m} m = g m$

Step 2.1.1.2

Rewrite the expression.

$t + m f = g m$

Step 2.1.2

Simplify with commuting.

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Step 2.1.2.1

Reorder $m$ and $f$ .

$t + f m = g m$

Step 2.1.2.2

Reorder $t$ and $f m$ .

$f m + t = g m$

Step 3

Subtract $f m$ from both sides of the equation.

$t = g m - f m$

Step 4

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$