Solve x+10/9-xx^2-5x-36/4x^2+16x

$$\frac{ x+10 }{ 9-x } \frac{ { x }^{ 2 } -5x-36 }{ 4 { x }^{ 2 } +16x }$$

Evaluate

$$-\frac{1}{4}-\frac{5}{2x}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}-5x-36}{4x^{2}+16x}.

$$\frac{x+10}{9-x}\times \frac{\left(x-9\right)\left(x+4\right)}{4x\left(x+4\right)}$$

Cancel out x+4 in both numerator and denominator.

$$\frac{x+10}{9-x}\times \frac{x-9}{4x}$$

Multiply \frac{x+10}{9-x} times \frac{x-9}{4x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x+10\right)\left(x-9\right)}{\left(9-x\right)\times 4x}$$

Extract the negative sign in x-9.

$$\frac{-\left(x+10\right)\left(-x+9\right)}{4x\left(-x+9\right)}$$

Cancel out -x+9 in both numerator and denominator.

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

Cancel out -1 in both numerator and denominator.

$$\frac{x+10}{-4x}$$

Expand

$$-\frac{1}{4}-\frac{5}{2x}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}-5x-36}{4x^{2}+16x}.

$$\frac{x+10}{9-x}\times \frac{\left(x-9\right)\left(x+4\right)}{4x\left(x+4\right)}$$

Cancel out x+4 in both numerator and denominator.

$$\frac{x+10}{9-x}\times \frac{x-9}{4x}$$

Multiply \frac{x+10}{9-x} times \frac{x-9}{4x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x+10\right)\left(x-9\right)}{\left(9-x\right)\times 4x}$$

Extract the negative sign in x-9.

$$\frac{-\left(x+10\right)\left(-x+9\right)}{4x\left(-x+9\right)}$$

Cancel out -x+9 in both numerator and denominator.

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

Cancel out -1 in both numerator and denominator.

$$\frac{x+10}{-4x}$$