Algebra Examples

$\frac{d - 2}{d - 3} = \frac{1}{- m}$

Step 1

Cancel the common factor of $1$ and $- 1$ .

Tap for more steps...

Step 1.1

Rewrite $1$ as $- 1 (- 1)$ .

$\frac{d - 2}{d - 3} = \frac{- 1 (- 1)}{- m}$

Step 1.2

Move the negative in front of the fraction.

$\frac{d - 2}{d - 3} = - \frac{1}{m}$

Step 2

Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.

$(d - 2) m = (d - 3) \cdot - 1$

Step 3

Solve the equation for $d$ .

Tap for more steps...

Step 3.1

Simplify $(d - 2) m$ .

Tap for more steps...

Step 3.1.1

Rewrite.

$0 + 0 + (d - 2) m = (d - 3) \cdot - 1$

Step 3.1.2

Simplify by adding zeros.

$(d - 2) m = (d - 3) \cdot - 1$

Step 3.1.3

Apply the distributive property.

$d m - 2 m = (d - 3) \cdot - 1$

Step 3.2

Simplify $(d - 3) \cdot - 1$ .

Tap for more steps...

Step 3.2.1

Simplify by multiplying through.

Tap for more steps...

Step 3.2.1.1

Apply the distributive property.

$d m - 2 m = d \cdot - 1 - 3 \cdot - 1$

Step 3.2.1.2

Simplify the expression.

Tap for more steps...

Step 3.2.1.2.1

Move $- 1$ to the left of $d$ .

$d m - 2 m = - 1 \cdot d - 3 \cdot - 1$

Step 3.2.1.2.2

Multiply $- 3$ by $- 1$ .

$d m - 2 m = - 1 \cdot d + 3$

Step 3.2.2

Rewrite $- 1 d$ as $- d$ .

$d m - 2 m = - d + 3$

Step 3.3

Add $d$ to both sides of the equation.

$d m - 2 m + d = 3$

Step 3.4

Add $2 m$ to both sides of the equation.

$d m + d = 3 + 2 m$

Step 3.5

Factor $d$ out of $d m + d$ .

Tap for more steps...

Step 3.5.1

Factor $d$ out of $d m$ .

$d (m) + d = 3 + 2 m$

Step 3.5.2

Raise $d$ to the power of $1$ .

$d (m) + d = 3 + 2 m$

Step 3.5.3

Factor $d$ out of $d^{1}$ .

$d (m) + d \cdot 1 = 3 + 2 m$

Step 3.5.4

Factor $d$ out of $d (m) + d \cdot 1$ .

$d (m + 1) = 3 + 2 m$

Step 3.6

Divide each term in $d (m + 1) = 3 + 2 m$ by $m + 1$ and simplify.

Tap for more steps...

Step 3.6.1

Divide each term in $d (m + 1) = 3 + 2 m$ by $m + 1$ .

$\frac{d (m + 1)}{m + 1} = \frac{3}{m + 1} + \frac{2 m}{m + 1}$

Step 3.6.2

Simplify the left side.

Tap for more steps...

Step 3.6.2.1

Cancel the common factor of $m + 1$ .

Tap for more steps...

Step 3.6.2.1.1

Cancel the common factor.

$\frac{d (m + 1)}{m + 1} = \frac{3}{m + 1} + \frac{2 m}{m + 1}$

Step 3.6.2.1.2

Divide $d$ by $1$ .

$d = \frac{3}{m + 1} + \frac{2 m}{m + 1}$

Step 3.6.3

Simplify the right side.

Tap for more steps...

Step 3.6.3.1

Combine the numerators over the common denominator.

$d = \frac{3 + 2 m}{m + 1}$