Algebra Examples

$\frac{b}{a} x = \frac{d}{c} + 1$

Step 1

Move all terms containing variables to the left side of the equation.

Tap for more steps...

Step 1.1

Subtract $\frac{d}{c}$ from both sides of the equation.

$\frac{b}{a} \cdot x - \frac{d}{c} = 1$

Step 1.2

Combine $\frac{b}{a}$ and $x$ .

$\frac{b x}{a} - \frac{d}{c} = 1$

Step 2

Add $\frac{d}{c}$ to both sides of the equation.

$\frac{b x}{a} = 1 + \frac{d}{c}$

Step 3

Multiply both sides by $a$ .

$\frac{b x}{a} a = (1 + \frac{d}{c}) a$

Step 4

Simplify.

Tap for more steps...

Step 4.1

Simplify the left side.

Tap for more steps...

Step 4.1.1

Cancel the common factor of $a$ .

Tap for more steps...

Step 4.1.1.1

Cancel the common factor.

$\frac{b x}{a} a = (1 + \frac{d}{c}) a$

Step 4.1.1.2

Rewrite the expression.

$b x = (1 + \frac{d}{c}) a$

Step 4.2

Simplify the right side.

Tap for more steps...

Step 4.2.1

Simplify $(1 + \frac{d}{c}) a$ .

Tap for more steps...

Step 4.2.1.1

Apply the distributive property.

$b x = 1 a + \frac{d}{c} a$

Step 4.2.1.2

Multiply $a$ by $1$ .

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

Step 4.2.1.3

Combine $\frac{d}{c}$ and $a$ .

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

Step 4.2.1.4

Simplify with commuting.

Tap for more steps...

Step 4.2.1.4.1

Reorder $d$ and $a$ .

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

Step 4.2.1.4.2

Reorder $a$ and $\frac{a d}{c}$ .

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

Step 5

Divide each term in $b x = \frac{a d}{c} + a$ by $b$ and simplify.

Tap for more steps...

Step 5.1

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

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

Step 5.2

Simplify the left side.

Tap for more steps...

Step 5.2.1

Cancel the common factor of $b$ .

Tap for more steps...

Step 5.2.1.1

Cancel the common factor.

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

Step 5.2.1.2

Divide $x$ by $1$ .

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

Step 5.3

Simplify the right side.

Tap for more steps...

Step 5.3.1

Simplify each term.

Tap for more steps...

Step 5.3.1.1

Multiply the numerator by the reciprocal of the denominator.

$x = \frac{a d}{c} \cdot \frac{1}{b} + \frac{a}{b}$

Step 5.3.1.2

Multiply $\frac{a d}{c}$ by $\frac{1}{b}$ .

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