Solve x^2+10x+25/x^2-8x+16*x^2-16/x^2-25

$$\frac { x ^ { 2 } + 10 x + 25 } { x ^ { 2 } - 8 x + 16 } \times \frac { x ^ { 2 } - 16 } { x ^ { 2 } - 25 }$$

Evaluate

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

Short Solution Steps

Multiply \frac{x^{2}+10x+25}{x^{2}-8x+16} times \frac{x^{2}-16}{x^{2}-25} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x^{2}+10x+25\right)\left(x^{2}-16\right)}{\left(x^{2}-8x+16\right)\left(x^{2}-25\right)}$$

Factor the expressions that are not already factored.

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

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

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

Expand the expression.

$$\frac{x^{2}+9x+20}{x^{2}-9x+20}$$

Expand

$$\frac{x^{2}+9x+20}{\left(x-5\right)\left(x-4\right)}$$

Short Solution Steps

Multiply \frac{x^{2}+10x+25}{x^{2}-8x+16} times \frac{x^{2}-16}{x^{2}-25} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x^{2}+10x+25\right)\left(x^{2}-16\right)}{\left(x^{2}-8x+16\right)\left(x^{2}-25\right)}$$

Factor the expressions that are not already factored.

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

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

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

Expand the expression.

$$\frac{x^{2}+9x+20}{x^{2}-9x+20}$$