Solve frac{2x^{2}-7x+6}{3x^{2}-2x-8}*2x^2+7x+5/4x^2+5x-6*3x^2+7x+4/x^2+4x+4

$$\frac { 2 x ^ { 2 } - 7 x + 6 } { 3 x ^ { 2 } - 2 x - 8 } \cdot \frac { 2 x ^ { 2 } + 7 x + 5 } { 4 x ^ { 2 } + 5 x - 6 } \cdot \frac { 3 x ^ { 2 } + 7 x + 4 } { x ^ { 2 } + 4 x + 4 }$$

Evaluate

$$\frac{\left(2x-3\right)\left(2x+5\right)\left(x+1\right)^{2}}{\left(4x-3\right)\left(x+2\right)^{3}}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{2x^{2}-7x+6}{3x^{2}-2x-8}.

$$\frac{\left(x-2\right)\left(2x-3\right)}{\left(x-2\right)\left(3x+4\right)}\times \frac{2x^{2}+7x+5}{4x^{2}+5x-6}\times \frac{3x^{2}+7x+4}{x^{2}+4x+4}$$

Cancel out x-2 in both numerator and denominator.

$$\frac{2x-3}{3x+4}\times \frac{2x^{2}+7x+5}{4x^{2}+5x-6}\times \frac{3x^{2}+7x+4}{x^{2}+4x+4}$$

Multiply \frac{2x-3}{3x+4} times \frac{2x^{2}+7x+5}{4x^{2}+5x-6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(2x-3\right)\left(2x^{2}+7x+5\right)}{\left(3x+4\right)\left(4x^{2}+5x-6\right)}\times \frac{3x^{2}+7x+4}{x^{2}+4x+4}$$

Multiply \frac{\left(2x-3\right)\left(2x^{2}+7x+5\right)}{\left(3x+4\right)\left(4x^{2}+5x-6\right)} times \frac{3x^{2}+7x+4}{x^{2}+4x+4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(2x-3\right)\left(2x^{2}+7x+5\right)\left(3x^{2}+7x+4\right)}{\left(3x+4\right)\left(4x^{2}+5x-6\right)\left(x^{2}+4x+4\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(2x-3\right)\left(2x+5\right)\left(3x+4\right)\left(x+1\right)^{2}}{\left(4x-3\right)\left(x+2\right)\left(3x+4\right)\left(x+2\right)^{2}}$$

Cancel out 3x+4 in both numerator and denominator.

$$\frac{\left(2x-3\right)\left(2x+5\right)\left(x+1\right)^{2}}{\left(4x-3\right)\left(x+2\right)\left(x+2\right)^{2}}$$

Expand the expression.

$$\frac{4x^{4}+12x^{3}-3x^{2}-26x-15}{4x^{4}+21x^{3}+30x^{2}-4x-24}$$

Expand

$$\frac{4x^{4}+12x^{3}-3x^{2}-26x-15}{\left(4x^{2}+5x-6\right)\left(x^{2}+4x+4\right)}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{2x^{2}-7x+6}{3x^{2}-2x-8}.

$$\frac{\left(x-2\right)\left(2x-3\right)}{\left(x-2\right)\left(3x+4\right)}\times \frac{2x^{2}+7x+5}{4x^{2}+5x-6}\times \frac{3x^{2}+7x+4}{x^{2}+4x+4}$$

Cancel out x-2 in both numerator and denominator.

$$\frac{2x-3}{3x+4}\times \frac{2x^{2}+7x+5}{4x^{2}+5x-6}\times \frac{3x^{2}+7x+4}{x^{2}+4x+4}$$

Multiply \frac{2x-3}{3x+4} times \frac{2x^{2}+7x+5}{4x^{2}+5x-6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(2x-3\right)\left(2x^{2}+7x+5\right)}{\left(3x+4\right)\left(4x^{2}+5x-6\right)}\times \frac{3x^{2}+7x+4}{x^{2}+4x+4}$$

Multiply \frac{\left(2x-3\right)\left(2x^{2}+7x+5\right)}{\left(3x+4\right)\left(4x^{2}+5x-6\right)} times \frac{3x^{2}+7x+4}{x^{2}+4x+4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(2x-3\right)\left(2x^{2}+7x+5\right)\left(3x^{2}+7x+4\right)}{\left(3x+4\right)\left(4x^{2}+5x-6\right)\left(x^{2}+4x+4\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(2x-3\right)\left(2x+5\right)\left(3x+4\right)\left(x+1\right)^{2}}{\left(4x-3\right)\left(x+2\right)\left(3x+4\right)\left(x+2\right)^{2}}$$

Cancel out 3x+4 in both numerator and denominator.

$$\frac{\left(2x-3\right)\left(2x+5\right)\left(x+1\right)^{2}}{\left(4x-3\right)\left(x+2\right)\left(x+2\right)^{2}}$$

Expand the expression.

$$\frac{4x^{4}+12x^{3}-3x^{2}-26x-15}{4x^{4}+21x^{3}+30x^{2}-4x-24}$$