Solve x^2+9x+20/x^2-15x+44*x^2-11x+28/x^2+12x+35

$$\frac { x ^ { 2 } + 9 x + 20 } { x ^ { 2 } - 15 x + 44 } \cdot \frac { x ^ { 2 } - 11 x + 28 } { x ^ { 2 } + 12 x + 35 }$$

Evaluate

$$\frac{\left(x-7\right)\left(x+4\right)}{\left(x-11\right)\left(x+7\right)}$$

Short Solution Steps

Multiply \frac{x^{2}+9x+20}{x^{2}-15x+44} times \frac{x^{2}-11x+28}{x^{2}+12x+35} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x^{2}+9x+20\right)\left(x^{2}-11x+28\right)}{\left(x^{2}-15x+44\right)\left(x^{2}+12x+35\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(x-7\right)\left(x-4\right)\left(x+4\right)\left(x+5\right)}{\left(x-11\right)\left(x-4\right)\left(x+5\right)\left(x+7\right)}$$

Cancel out \left(x-4\right)\left(x+5\right) in both numerator and denominator.

$$\frac{\left(x-7\right)\left(x+4\right)}{\left(x-11\right)\left(x+7\right)}$$

Expand the expression.

$$\frac{x^{2}-3x-28}{x^{2}-4x-77}$$

Expand

$$\frac{x^{2}-3x-28}{\left(x-11\right)\left(x+7\right)}$$

Short Solution Steps

Multiply \frac{x^{2}+9x+20}{x^{2}-15x+44} times \frac{x^{2}-11x+28}{x^{2}+12x+35} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x^{2}+9x+20\right)\left(x^{2}-11x+28\right)}{\left(x^{2}-15x+44\right)\left(x^{2}+12x+35\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(x-7\right)\left(x-4\right)\left(x+4\right)\left(x+5\right)}{\left(x-11\right)\left(x-4\right)\left(x+5\right)\left(x+7\right)}$$

Cancel out \left(x-4\right)\left(x+5\right) in both numerator and denominator.

$$\frac{\left(x-7\right)\left(x+4\right)}{\left(x-11\right)\left(x+7\right)}$$

Expand the expression.

$$\frac{x^{2}-3x-28}{x^{2}-4x-77}$$