Algebra Examples

$y = \frac{a x + b}{c x + d}$

Step 1

Rewrite the equation as $\frac{a x + b}{c x + d} = y$ .

$\frac{a x + b}{c x + d} = y$

Step 2

Find the LCD of the terms in the equation.

Tap for more steps...

Step 2.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$c x + d, 1$

Step 2.2

Remove parentheses.

$c x + d, 1$

Step 2.3

The LCM of one and any expression is the expression.

$c x + d$

Step 3

Multiply each term in $\frac{a x + b}{c x + d} = y$ by $c x + d$ to eliminate the fractions.

Tap for more steps...

Step 3.1

Multiply each term in $\frac{a x + b}{c x + d} = y$ by $c x + d$ .

$\frac{a x + b}{c x + d} (c x + d) = y (c x + d)$

Step 3.2

Simplify the left side.

Tap for more steps...

Step 3.2.1

Cancel the common factor of $c x + d$ .

Tap for more steps...

Step 3.2.1.1

Cancel the common factor.

$\frac{a x + b}{c x + d} (c x + d) = y (c x + d)$

Step 3.2.1.2

Rewrite the expression.

$a x + b = y (c x + d)$

Step 3.3

Simplify the right side.

Tap for more steps...

Step 3.3.1

Apply the distributive property.

$a x + b = y c x + y d$

Step 4

Solve the equation.

Tap for more steps...

Step 4.1

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

$a x + b - y c x = y d$

Step 4.2

Subtract $b$ from both sides of the equation.

$a x - y c x = y d - b$

Step 4.3

Factor $x$ out of $a x - y c x$ .

Tap for more steps...

Step 4.3.1

Factor $x$ out of $a x$ .

$x a - y c x = y d - b$

Step 4.3.2

Factor $x$ out of $- y c x$ .

$x a + x (- y c) = y d - b$

Step 4.3.3

Factor $x$ out of $x a + x (- y c)$ .

$x (a - y c) = y d - b$

Step 4.4

Divide each term in $x (a - y c) = y d - b$ by $a - y c$ and simplify.

Tap for more steps...

Step 4.4.1

Divide each term in $x (a - y c) = y d - b$ by $a - y c$ .

$\frac{x (a - y c)}{a - y c} = \frac{y d}{a - y c} + \frac{- b}{a - y c}$

Step 4.4.2

Simplify the left side.

Tap for more steps...

Step 4.4.2.1

Cancel the common factor of $a - y c$ .

Tap for more steps...

Step 4.4.2.1.1

Cancel the common factor.

$\frac{x (a - y c)}{a - y c} = \frac{y d}{a - y c} + \frac{- b}{a - y c}$

Step 4.4.2.1.2

Divide $x$ by $1$ .

$x = \frac{y d}{a - y c} + \frac{- b}{a - y c}$

Step 4.4.3

Simplify the right side.

Tap for more steps...

Step 4.4.3.1

Move the negative in front of the fraction.

$x = \frac{y d}{a - y c} - \frac{b}{a - y c}$

Step 4.4.3.2

Combine the numerators over the common denominator.

$x = \frac{y d - b}{a - y c}$