Solve 7/b-16/b+9/frac{9{b}+9/b+9}

$$\frac { \frac { 7 } { b } - \frac { 16 } { b + 9 } } { \frac { 9 } { b } + \frac { 9 } { b + 9 } }$$

Evaluate

$$\frac{7-b}{2b+9}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of b and b+9 is b\left(b+9\right). Multiply \frac{7}{b} times \frac{b+9}{b+9}. Multiply \frac{16}{b+9} times \frac{b}{b}.

$$\frac{\frac{7\left(b+9\right)}{b\left(b+9\right)}-\frac{16b}{b\left(b+9\right)}}{\frac{9}{b}+\frac{9}{b+9}}$$

Since \frac{7\left(b+9\right)}{b\left(b+9\right)} and \frac{16b}{b\left(b+9\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{7\left(b+9\right)-16b}{b\left(b+9\right)}}{\frac{9}{b}+\frac{9}{b+9}}$$

Do the multiplications in 7\left(b+9\right)-16b.

$$\frac{\frac{7b+63-16b}{b\left(b+9\right)}}{\frac{9}{b}+\frac{9}{b+9}}$$

Combine like terms in 7b+63-16b.

$$\frac{\frac{-9b+63}{b\left(b+9\right)}}{\frac{9}{b}+\frac{9}{b+9}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of b and b+9 is b\left(b+9\right). Multiply \frac{9}{b} times \frac{b+9}{b+9}. Multiply \frac{9}{b+9} times \frac{b}{b}.

$$\frac{\frac{-9b+63}{b\left(b+9\right)}}{\frac{9\left(b+9\right)}{b\left(b+9\right)}+\frac{9b}{b\left(b+9\right)}}$$

Since \frac{9\left(b+9\right)}{b\left(b+9\right)} and \frac{9b}{b\left(b+9\right)} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-9b+63}{b\left(b+9\right)}}{\frac{9\left(b+9\right)+9b}{b\left(b+9\right)}}$$

Do the multiplications in 9\left(b+9\right)+9b.

$$\frac{\frac{-9b+63}{b\left(b+9\right)}}{\frac{9b+81+9b}{b\left(b+9\right)}}$$

Combine like terms in 9b+81+9b.

$$\frac{\frac{-9b+63}{b\left(b+9\right)}}{\frac{18b+81}{b\left(b+9\right)}}$$

Divide \frac{-9b+63}{b\left(b+9\right)} by \frac{18b+81}{b\left(b+9\right)} by multiplying \frac{-9b+63}{b\left(b+9\right)} by the reciprocal of \frac{18b+81}{b\left(b+9\right)}.

$$\frac{\left(-9b+63\right)b\left(b+9\right)}{b\left(b+9\right)\left(18b+81\right)}$$

Cancel out b\left(b+9\right) in both numerator and denominator.

$$\frac{-9b+63}{18b+81}$$

Factor the expressions that are not already factored.

$$\frac{9\left(-b+7\right)}{9\left(2b+9\right)}$$

Cancel out 9 in both numerator and denominator.

$$\frac{-b+7}{2b+9}$$

Expand

$$-\frac{b-7}{2b+9}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of b and b+9 is b\left(b+9\right). Multiply \frac{7}{b} times \frac{b+9}{b+9}. Multiply \frac{16}{b+9} times \frac{b}{b}.

$$\frac{\frac{7\left(b+9\right)}{b\left(b+9\right)}-\frac{16b}{b\left(b+9\right)}}{\frac{9}{b}+\frac{9}{b+9}}$$

Since \frac{7\left(b+9\right)}{b\left(b+9\right)} and \frac{16b}{b\left(b+9\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{7\left(b+9\right)-16b}{b\left(b+9\right)}}{\frac{9}{b}+\frac{9}{b+9}}$$

Do the multiplications in 7\left(b+9\right)-16b.

$$\frac{\frac{7b+63-16b}{b\left(b+9\right)}}{\frac{9}{b}+\frac{9}{b+9}}$$

Combine like terms in 7b+63-16b.

$$\frac{\frac{-9b+63}{b\left(b+9\right)}}{\frac{9}{b}+\frac{9}{b+9}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of b and b+9 is b\left(b+9\right). Multiply \frac{9}{b} times \frac{b+9}{b+9}. Multiply \frac{9}{b+9} times \frac{b}{b}.

$$\frac{\frac{-9b+63}{b\left(b+9\right)}}{\frac{9\left(b+9\right)}{b\left(b+9\right)}+\frac{9b}{b\left(b+9\right)}}$$

Since \frac{9\left(b+9\right)}{b\left(b+9\right)} and \frac{9b}{b\left(b+9\right)} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-9b+63}{b\left(b+9\right)}}{\frac{9\left(b+9\right)+9b}{b\left(b+9\right)}}$$

Do the multiplications in 9\left(b+9\right)+9b.

$$\frac{\frac{-9b+63}{b\left(b+9\right)}}{\frac{9b+81+9b}{b\left(b+9\right)}}$$

Combine like terms in 9b+81+9b.

$$\frac{\frac{-9b+63}{b\left(b+9\right)}}{\frac{18b+81}{b\left(b+9\right)}}$$

Divide \frac{-9b+63}{b\left(b+9\right)} by \frac{18b+81}{b\left(b+9\right)} by multiplying \frac{-9b+63}{b\left(b+9\right)} by the reciprocal of \frac{18b+81}{b\left(b+9\right)}.

$$\frac{\left(-9b+63\right)b\left(b+9\right)}{b\left(b+9\right)\left(18b+81\right)}$$

Cancel out b\left(b+9\right) in both numerator and denominator.

$$\frac{-9b+63}{18b+81}$$

Factor the expressions that are not already factored.

$$\frac{9\left(-b+7\right)}{9\left(2b+9\right)}$$

Cancel out 9 in both numerator and denominator.

$$\frac{-b+7}{2b+9}$$