Solve by Factoring 7/9=b/(b-10)

$\frac{7}{9} = \frac{b}{b - 10}$

Step 1

Subtract $\frac{b}{b - 10}$ from both sides of the equation.

$\frac{7}{9} - \frac{b}{b - 10} = 0$

Step 2

Simplify $\frac{7}{9} - \frac{b}{b - 10}$ .

To write $\frac{7}{9}$ as a fraction with a common denominator, multiply by $\frac{b - 10}{b - 10}$ .

$\frac{7}{9} \cdot \frac{b - 10}{b - 10} - \frac{b}{b - 10} = 0$

To write $- \frac{b}{b - 10}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{7}{9} \cdot \frac{b - 10}{b - 10} - \frac{b}{b - 10} \cdot \frac{9}{9} = 0$

Write each expression with a common denominator of $9 (b - 10)$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{7}{9}$ by $\frac{b - 10}{b - 10}$ .

$\frac{7 (b - 10)}{9 (b - 10)} - \frac{b}{b - 10} \cdot \frac{9}{9} = 0$

Multiply $\frac{b}{b - 10}$ by $\frac{9}{9}$ .

$\frac{7 (b - 10)}{9 (b - 10)} - \frac{b \cdot 9}{(b - 10) \cdot 9} = 0$

Reorder the factors of $(b - 10) \cdot 9$ .

$\frac{7 (b - 10)}{9 (b - 10)} - \frac{b \cdot 9}{9 (b - 10)} = 0$

Combine the numerators over the common denominator.

$\frac{7 (b - 10) - b \cdot 9}{9 (b - 10)} = 0$

Simplify the numerator.

Apply the distributive property.

$\frac{7 b + 7 \cdot - 10 - b \cdot 9}{9 (b - 10)} = 0$

Multiply $7$ by $- 10$ .

$\frac{7 b - 70 - b \cdot 9}{9 (b - 10)} = 0$

Multiply $9$ by $- 1$ .

$\frac{7 b - 70 - 9 b}{9 (b - 10)} = 0$

Subtract $9 b$ from $7 b$ .

$\frac{- 2 b - 70}{9 (b - 10)} = 0$

Factor $2$ out of $- 2 b - 70$ .

Factor $2$ out of $- 2 b$ .

$\frac{2 (- b) - 70}{9 (b - 10)} = 0$

Factor $2$ out of $- 70$ .

$\frac{2 (- b) + 2 (- 35)}{9 (b - 10)} = 0$

Factor $2$ out of $2 (- b) + 2 (- 35)$ .

$\frac{2 (- b - 35)}{9 (b - 10)} = 0$

Factor $- 1$ out of $- b$ .

$\frac{2 (- (b) - 35)}{9 (b - 10)} = 0$

Rewrite $- 35$ as $- 1 (35)$ .

$\frac{2 (- (b) - 1 (35))}{9 (b - 10)} = 0$

Factor $- 1$ out of $- (b) - 1 (35)$ .

$\frac{2 (- (b + 35))}{9 (b - 10)} = 0$

Rewrite $- (b + 35)$ as $- 1 (b + 35)$ .

$\frac{2 (- 1 (b + 35))}{9 (b - 10)} = 0$

Move the negative in front of the fraction.

$- \frac{2 (b + 35)}{9 (b - 10)} = 0$

Step 3

Set the numerator equal to zero.

$2 (b + 35) = 0$

Step 4

Solve the equation for $b$ .

Divide each term in $2 (b + 35) = 0$ by $2$ and simplify.

Divide each term in $2 (b + 35) = 0$ by $2$ .

$\frac{2 (b + 35)}{2} = \frac{0}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 (b + 35)}{2} = \frac{0}{2}$

Divide $b + 35$ by $1$ .

$b + 35 = \frac{0}{2}$

Simplify the right side.

Divide $0$ by $2$ .

$b + 35 = 0$

Subtract $35$ from both sides of the equation.

$b = - 35$

Solve by Factoring 7/9=b/(b-10)

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