Simplify 5/b-7/9+6/(b^2)

$\frac{5}{b} - \frac{7}{9} + \frac{6}{b^{2}}$

To write $\frac{5}{b}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{5}{b} \cdot \frac{9}{9} - \frac{7}{9} + \frac{6}{b^{2}}$

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

$\frac{5}{b} \cdot \frac{9}{9} - \frac{7}{9} \cdot \frac{b}{b} + \frac{6}{b^{2}}$

Write each expression with a common denominator of $b \cdot 9$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{5}{b}$ by $\frac{9}{9}$ .

$\frac{5 \cdot 9}{b \cdot 9} - \frac{7}{9} \cdot \frac{b}{b} + \frac{6}{b^{2}}$

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

$\frac{5 \cdot 9}{b \cdot 9} - \frac{7 b}{9 b} + \frac{6}{b^{2}}$

Reorder the factors of $b \cdot 9$ .

$\frac{5 \cdot 9}{9 b} - \frac{7 b}{9 b} + \frac{6}{b^{2}}$

Combine the numerators over the common denominator.

$\frac{5 \cdot 9 - 7 b}{9 b} + \frac{6}{b^{2}}$

Multiply $5$ by $9$ .

$\frac{45 - 7 b}{9 b} + \frac{6}{b^{2}}$

To write $\frac{45 - 7 b}{9 b}$ as a fraction with a common denominator, multiply by $\frac{b}{b}$ .

$\frac{45 - 7 b}{9 b} \cdot \frac{b}{b} + \frac{6}{b^{2}}$

To write $\frac{6}{b^{2}}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{45 - 7 b}{9 b} \cdot \frac{b}{b} + \frac{6}{b^{2}} \cdot \frac{9}{9}$

Write each expression with a common denominator of $9 b^{2}$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{45 - 7 b}{9 b}$ by $\frac{b}{b}$ .

$\frac{(45 - 7 b) b}{9 b \cdot b} + \frac{6}{b^{2}} \cdot \frac{9}{9}$

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

$\frac{(45 - 7 b) b}{9 (b^{1} b)} + \frac{6}{b^{2}} \cdot \frac{9}{9}$

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

$\frac{(45 - 7 b) b}{9 (b^{1} b^{1})} + \frac{6}{b^{2}} \cdot \frac{9}{9}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{(45 - 7 b) b}{9 b^{1 + 1}} + \frac{6}{b^{2}} \cdot \frac{9}{9}$

Add $1$ and $1$ .

$\frac{(45 - 7 b) b}{9 b^{2}} + \frac{6}{b^{2}} \cdot \frac{9}{9}$

Multiply $\frac{6}{b^{2}}$ by $\frac{9}{9}$ .

$\frac{(45 - 7 b) b}{9 b^{2}} + \frac{6 \cdot 9}{b^{2} \cdot 9}$

Reorder the factors of $b^{2} \cdot 9$ .

$\frac{(45 - 7 b) b}{9 b^{2}} + \frac{6 \cdot 9}{9 b^{2}}$

Combine the numerators over the common denominator.

$\frac{(45 - 7 b) b + 6 \cdot 9}{9 b^{2}}$

Simplify the numerator.

Apply the distributive property.

$\frac{45 b - 7 b \cdot b + 6 \cdot 9}{9 b^{2}}$

Multiply $b$ by $b$ by adding the exponents.

Move $b$ .

$\frac{45 b - 7 (b \cdot b) + 6 \cdot 9}{9 b^{2}}$

Multiply $b$ by $b$ .

$\frac{45 b - 7 b^{2} + 6 \cdot 9}{9 b^{2}}$

Multiply $6$ by $9$ .

$\frac{45 b - 7 b^{2} + 54}{9 b^{2}}$

Reorder terms.

$\frac{- 7 b^{2} + 45 b + 54}{9 b^{2}}$

Simplify with factoring out.

Factor $- 1$ out of $- 7 b^{2}$ .

$\frac{- (7 b^{2}) + 45 b + 54}{9 b^{2}}$

Factor $- 1$ out of $45 b$ .

$\frac{- (7 b^{2}) - (- 45 b) + 54}{9 b^{2}}$

Factor $- 1$ out of $- (7 b^{2}) - (- 45 b)$ .

$\frac{- (7 b^{2} - 45 b) + 54}{9 b^{2}}$

Rewrite $54$ as $- 1 (- 54)$ .

$\frac{- (7 b^{2} - 45 b) - 1 (- 54)}{9 b^{2}}$

Factor $- 1$ out of $- (7 b^{2} - 45 b) - 1 (- 54)$ .

$\frac{- (7 b^{2} - 45 b - 54)}{9 b^{2}}$

Simplify the expression.

Rewrite $- (7 b^{2} - 45 b - 54)$ as $- 1 (7 b^{2} - 45 b - 54)$ .

$\frac{- 1 (7 b^{2} - 45 b - 54)}{9 b^{2}}$

Move the negative in front of the fraction.

$- \frac{7 b^{2} - 45 b - 54}{9 b^{2}}$

Simplify 5/b-7/9+6/(b^2)

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