Solve x^2-10x+16/x^2-9x+20div4-x^2/x^2+6x-40

$$\frac { x ^ { 2 } - 10 x + 16 } { x ^ { 2 } - 9 x + 20 } \div \frac { 4 - x ^ { 2 } } { x ^ { 2 } + 6 x - 40 }$$

Evaluate

$$-\frac{\left(x-8\right)\left(x+10\right)}{\left(x-5\right)\left(x+2\right)}$$

Short Solution Steps

Divide \frac{x^{2}-10x+16}{x^{2}-9x+20} by \frac{4-x^{2}}{x^{2}+6x-40} by multiplying \frac{x^{2}-10x+16}{x^{2}-9x+20} by the reciprocal of \frac{4-x^{2}}{x^{2}+6x-40}.

$$\frac{\left(x^{2}-10x+16\right)\left(x^{2}+6x-40\right)}{\left(x^{2}-9x+20\right)\left(4-x^{2}\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(x-8\right)\left(x-4\right)\left(x-2\right)\left(x+10\right)}{\left(x-5\right)\left(x-4\right)\left(x-2\right)\left(-x-2\right)}$$

Cancel out \left(x-4\right)\left(x-2\right) in both numerator and denominator.

$$\frac{\left(x-8\right)\left(x+10\right)}{\left(x-5\right)\left(-x-2\right)}$$

Expand the expression.

$$\frac{x^{2}+2x-80}{-x^{2}+3x+10}$$

Expand

$$-\frac{x^{2}+2x-80}{\left(x-5\right)\left(x+2\right)}$$

Short Solution Steps

Divide \frac{x^{2}-10x+16}{x^{2}-9x+20} by \frac{4-x^{2}}{x^{2}+6x-40} by multiplying \frac{x^{2}-10x+16}{x^{2}-9x+20} by the reciprocal of \frac{4-x^{2}}{x^{2}+6x-40}.

$$\frac{\left(x^{2}-10x+16\right)\left(x^{2}+6x-40\right)}{\left(x^{2}-9x+20\right)\left(4-x^{2}\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(x-8\right)\left(x-4\right)\left(x-2\right)\left(x+10\right)}{\left(x-5\right)\left(x-4\right)\left(x-2\right)\left(-x-2\right)}$$

Cancel out \left(x-4\right)\left(x-2\right) in both numerator and denominator.

$$\frac{\left(x-8\right)\left(x+10\right)}{\left(x-5\right)\left(-x-2\right)}$$

Expand the expression.

$$\frac{x^{2}+2x-80}{-x^{2}+3x+10}$$