Solve for d (d-2)/(d-3)=1/(-m)

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

Step 1

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

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

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

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 $d$ .

Simplify $(d - 2) m$ .

Start simplifying.

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

Simplify by adding zeros.

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

Apply the distributive property.

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

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

Simplify by multiplying through.

Apply the distributive property.

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

Simplify the expression.

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

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

Multiply $- 3$ by $- 1$ .

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

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

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

Add $d$ to both sides of the equation.

$d m - 2 m + d = 3$

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

$d m + d = 3 + 2 m$

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

Factor $d$ out of $d m$ .

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

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

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

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

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

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

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

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

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

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

Simplify the left side.

Cancel the common factor of $m + 1$ .

Cancel the common factor.

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

Divide $d$ by $1$ .

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

Simplify the right side.

Combine the numerators over the common denominator.

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

Solve for d (d-2)/(d-3)=1/(-m)

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