Algebra Examples

$\frac{y (x - a)}{z} = t$

Step 1

Multiply both sides by $z$ .

$\frac{y (x - a)}{z} z = t z$

Step 2

Simplify the left side.

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Step 2.1

Simplify $\frac{y (x - a)}{z} z$ .

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Step 2.1.1

Cancel the common factor of $z$ .

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Step 2.1.1.1

Cancel the common factor.

$\frac{y (x - a)}{z} z = t z$

Step 2.1.1.2

Rewrite the expression.

$y (x - a) = t z$

Step 2.1.2

Apply the distributive property.

$y x + y (- a) = t z$

Step 2.1.3

Simplify the expression.

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Step 2.1.3.1

Rewrite using the commutative property of multiplication.

$y x - y a = t z$

Step 2.1.3.2

Reorder $y$ and $x$ .

$x y - y a = t z$

Step 2.1.3.3

Move $y$ .

$x y - a y = t z$

Step 2.1.3.4

Reorder $x y$ and $- a y$ .

$- a y + x y = t z$

Step 3

Solve for $a$ .

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Step 3.1

Subtract $x y$ from both sides of the equation.

$- a y = t z - x y$

Step 3.2

Divide each term in $- a y = t z - x y$ by $- y$ and simplify.

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Step 3.2.1

Divide each term in $- a y = t z - x y$ by $- y$ .

$\frac{- a y}{- y} = \frac{t z}{- y} + \frac{- x y}{- y}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Dividing two negative values results in a positive value.

$\frac{a y}{y} = \frac{t z}{- y} + \frac{- x y}{- y}$

Step 3.2.2.2

Cancel the common factor of $y$ .

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Step 3.2.2.2.1

Cancel the common factor.

$\frac{a y}{y} = \frac{t z}{- y} + \frac{- x y}{- y}$

Step 3.2.2.2.2

Divide $a$ by $1$ .

$a = \frac{t z}{- y} + \frac{- x y}{- y}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Simplify each term.

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Step 3.2.3.1.1

Move the negative in front of the fraction.

$a = - \frac{t z}{y} + \frac{- x y}{- y}$

Step 3.2.3.1.2

Dividing two negative values results in a positive value.

$a = - \frac{t z}{y} + \frac{x y}{y}$

Step 3.2.3.1.3

Cancel the common factor of $y$ .

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Step 3.2.3.1.3.1

Cancel the common factor.

$a = - \frac{t z}{y} + \frac{x y}{y}$

Step 3.2.3.1.3.2

Divide $x$ by $1$ .

$a = - \frac{t z}{y} + x$