Linear Algebra Examples

$A X + B X = - C + D$

Step 1

Subtract $B X$ from both sides of the equation.

$A X = - C + D - B X$

Step 2

Divide each term in $A X = - C + D - B X$ by $X$ and simplify.

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Step 2.1

Divide each term in $A X = - C + D - B X$ by $X$ .

$\frac{A X}{X} = \frac{- C}{X} + \frac{D}{X} + \frac{- B X}{X}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $X$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{A X}{X} = \frac{- C}{X} + \frac{D}{X} + \frac{- B X}{X}$

Step 2.2.1.2

Divide $A$ by $1$ .

$A = \frac{- C}{X} + \frac{D}{X} + \frac{- B X}{X}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Move the negative in front of the fraction.

$A = - \frac{C}{X} + \frac{D}{X} + \frac{- B X}{X}$

Step 2.3.1.2

Cancel the common factor of $X$ .

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Step 2.3.1.2.1

Cancel the common factor.

$A = - \frac{C}{X} + \frac{D}{X} + \frac{- B X}{X}$

Step 2.3.1.2.2

Divide $- B$ by $1$ .

$A = - \frac{C}{X} + \frac{D}{X} - B$

Step 3

Set the denominator in $\frac{C}{X}$ equal to $0$ to find where the expression is undefined.

$X = 0$

Step 4

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

Interval Notation:

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

Set-Builder Notation:

${C | C \neq 0}$