Solve 1b^2-5b+6/3b-15*6b/b^2-b-30*b^2-25/2b-4

$$1 \frac { b ^ { 2 } - 5 b + 6 } { 3 b - 15 } \cdot \frac { 6 b } { b ^ { 2 } - b - 30 } \cdot \frac { b ^ { 2 } - 25 } { 2 b - 4 }$$

Evaluate

$$\frac{b\left(b-3\right)}{b-6}$$

Short Solution Steps

Express 1\times \frac{b^{2}-5b+6}{3b-15} as a single fraction.

$$\frac{b^{2}-5b+6}{3b-15}\times \frac{6b}{b^{2}-b-30}\times \frac{b^{2}-25}{2b-4}$$

Multiply \frac{b^{2}-5b+6}{3b-15} times \frac{6b}{b^{2}-b-30} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(b^{2}-5b+6\right)\times 6b}{\left(3b-15\right)\left(b^{2}-b-30\right)}\times \frac{b^{2}-25}{2b-4}$$

Multiply \frac{\left(b^{2}-5b+6\right)\times 6b}{\left(3b-15\right)\left(b^{2}-b-30\right)} times \frac{b^{2}-25}{2b-4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(b^{2}-5b+6\right)\times 6b\left(b^{2}-25\right)}{\left(3b-15\right)\left(b^{2}-b-30\right)\left(2b-4\right)}$$

Factor the expressions that are not already factored.

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

Cancel out 2\times 3\left(b-5\right)\left(b-2\right)\left(b+5\right) in both numerator and denominator.

$$\frac{b\left(b-3\right)}{b-6}$$

Expand the expression.

$$\frac{b^{2}-3b}{b-6}$$

Expand

$$\frac{b^{2}-3b}{b-6}$$

Short Solution Steps

Express 1\times \frac{b^{2}-5b+6}{3b-15} as a single fraction.

$$\frac{b^{2}-5b+6}{3b-15}\times \frac{6b}{b^{2}-b-30}\times \frac{b^{2}-25}{2b-4}$$

Multiply \frac{b^{2}-5b+6}{3b-15} times \frac{6b}{b^{2}-b-30} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(b^{2}-5b+6\right)\times 6b}{\left(3b-15\right)\left(b^{2}-b-30\right)}\times \frac{b^{2}-25}{2b-4}$$

Multiply \frac{\left(b^{2}-5b+6\right)\times 6b}{\left(3b-15\right)\left(b^{2}-b-30\right)} times \frac{b^{2}-25}{2b-4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(b^{2}-5b+6\right)\times 6b\left(b^{2}-25\right)}{\left(3b-15\right)\left(b^{2}-b-30\right)\left(2b-4\right)}$$

Factor the expressions that are not already factored.

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

Cancel out 2\times 3\left(b-5\right)\left(b-2\right)\left(b+5\right) in both numerator and denominator.

$$\frac{b\left(b-3\right)}{b-6}$$

Expand the expression.

$$\frac{b^{2}-3b}{b-6}$$