Solve b^2+4b+4/2b^2-8*3b-6/4b

$$\frac { b ^ { 2 } + 4 b + 4 } { 2 b ^ { 2 } - 8 } \cdot \frac { 3 b - 6 } { 4 b }$$

Evaluate

$$\frac{3}{8}+\frac{3}{4b}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{b^{2}+4b+4}{2b^{2}-8}.

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

Cancel out b+2 in both numerator and denominator.

$$\frac{b+2}{2\left(b-2\right)}\times \frac{3b-6}{4b}$$

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

$$\frac{\left(b+2\right)\left(3b-6\right)}{2\left(b-2\right)\times 4b}$$

Multiply 2 and 4 to get 8.

$$\frac{\left(b+2\right)\left(3b-6\right)}{8\left(b-2\right)b}$$

Factor the expressions that are not already factored.

$$\frac{3\left(b-2\right)\left(b+2\right)}{8b\left(b-2\right)}$$

Cancel out b-2 in both numerator and denominator.

$$\frac{3\left(b+2\right)}{8b}$$

Expand the expression.

$$\frac{3b+6}{8b}$$

Expand

$$\frac{3}{8}+\frac{3}{4b}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{b^{2}+4b+4}{2b^{2}-8}.

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

Cancel out b+2 in both numerator and denominator.

$$\frac{b+2}{2\left(b-2\right)}\times \frac{3b-6}{4b}$$

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

$$\frac{\left(b+2\right)\left(3b-6\right)}{2\left(b-2\right)\times 4b}$$

Multiply 2 and 4 to get 8.

$$\frac{\left(b+2\right)\left(3b-6\right)}{8\left(b-2\right)b}$$

Factor the expressions that are not already factored.

$$\frac{3\left(b-2\right)\left(b+2\right)}{8b\left(b-2\right)}$$

Cancel out b-2 in both numerator and denominator.

$$\frac{3\left(b+2\right)}{8b}$$

Expand the expression.

$$\frac{3b+6}{8b}$$