Linear Algebra Examples

$2 + x z = (x + 1) + z$

Step 1

Subtract $x$ from both sides of the equation.

$2 + x z - x = 1 + z$

Step 2

Move all terms not containing $x$ to the right side of the equation.

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Step 2.1

Subtract $2$ from both sides of the equation.

$x z - x = 1 + z - 2$

Step 2.2

Subtract $2$ from $1$ .

$x z - x = z - 1$

Step 3

Factor $x$ out of $x z - x$ .

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Step 3.1

Factor $x$ out of $x z$ .

$x (z) - x = z - 1$

Step 3.2

Factor $x$ out of $- x$ .

$x (z) + x \cdot - 1 = z - 1$

Step 3.3

Factor $x$ out of $x (z) + x \cdot - 1$ .

$x (z - 1) = z - 1$

Step 4

Divide each term in $x (z - 1) = z - 1$ by $z - 1$ and simplify.

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Step 4.1

Divide each term in $x (z - 1) = z - 1$ by $z - 1$ .

$\frac{x (z - 1)}{z - 1} = \frac{z}{z - 1} + \frac{- 1}{z - 1}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $z - 1$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{x (z - 1)}{z - 1} = \frac{z}{z - 1} + \frac{- 1}{z - 1}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{z}{z - 1} + \frac{- 1}{z - 1}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Combine the numerators over the common denominator.

$x = \frac{z - 1}{z - 1}$

Step 4.3.2

Cancel the common factor of $z - 1$ .

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Step 4.3.2.1

Cancel the common factor.

$x = \frac{z - 1}{z - 1}$

Step 4.3.2.2

Rewrite the expression.

$x = 1$

Step 5

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:

${x | x \in ℝ}$

Step 6