Solve 5b/b-3-b+6/2b-6*90/b^2+6b

$$\frac { 5 b } { b - 3 } - \frac { b + 6 } { 2 b - 6 } \cdot \frac { 90 } { b ^ { 2 } + 6 b }$$

Evaluate

$$5+\frac{15}{b}$$

Short Solution Steps

Multiply \frac{b+6}{2b-6} times \frac{90}{b^{2}+6b} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5b}{b-3}-\frac{\left(b+6\right)\times 90}{\left(2b-6\right)\left(b^{2}+6b\right)}$$

Factor the expressions that are not already factored in \frac{\left(b+6\right)\times 90}{\left(2b-6\right)\left(b^{2}+6b\right)}.

$$\frac{5b}{b-3}-\frac{90\left(b+6\right)}{2b\left(b-3\right)\left(b+6\right)}$$

Cancel out 2\left(b+6\right) in both numerator and denominator.

$$\frac{5b}{b-3}-\frac{45}{b\left(b-3\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of b-3 and b\left(b-3\right) is b\left(b-3\right). Multiply \frac{5b}{b-3} times \frac{b}{b}.

$$\frac{5bb}{b\left(b-3\right)}-\frac{45}{b\left(b-3\right)}$$

Since \frac{5bb}{b\left(b-3\right)} and \frac{45}{b\left(b-3\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5bb-45}{b\left(b-3\right)}$$

Do the multiplications in 5bb-45.

$$\frac{5b^{2}-45}{b\left(b-3\right)}$$

Factor the expressions that are not already factored in \frac{5b^{2}-45}{b\left(b-3\right)}.

$$\frac{5\left(b-3\right)\left(b+3\right)}{b\left(b-3\right)}$$

Cancel out b-3 in both numerator and denominator.

$$\frac{5\left(b+3\right)}{b}$$

Use the distributive property to multiply 5 by b+3.

$$\frac{5b+15}{b}$$

Expand

$$5+\frac{15}{b}$$

Short Solution Steps

Multiply \frac{b+6}{2b-6} times \frac{90}{b^{2}+6b} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5b}{b-3}-\frac{\left(b+6\right)\times 90}{\left(2b-6\right)\left(b^{2}+6b\right)}$$

Factor the expressions that are not already factored in \frac{\left(b+6\right)\times 90}{\left(2b-6\right)\left(b^{2}+6b\right)}.

$$\frac{5b}{b-3}-\frac{90\left(b+6\right)}{2b\left(b-3\right)\left(b+6\right)}$$

Cancel out 2\left(b+6\right) in both numerator and denominator.

$$\frac{5b}{b-3}-\frac{45}{b\left(b-3\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of b-3 and b\left(b-3\right) is b\left(b-3\right). Multiply \frac{5b}{b-3} times \frac{b}{b}.

$$\frac{5bb}{b\left(b-3\right)}-\frac{45}{b\left(b-3\right)}$$

Since \frac{5bb}{b\left(b-3\right)} and \frac{45}{b\left(b-3\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5bb-45}{b\left(b-3\right)}$$

Do the multiplications in 5bb-45.

$$\frac{5b^{2}-45}{b\left(b-3\right)}$$

Factor the expressions that are not already factored in \frac{5b^{2}-45}{b\left(b-3\right)}.

$$\frac{5\left(b-3\right)\left(b+3\right)}{b\left(b-3\right)}$$

Cancel out b-3 in both numerator and denominator.

$$\frac{5\left(b+3\right)}{b}$$

Use the distributive property to multiply 5 by b+3.

$$\frac{5b+15}{b}$$