Solve r^2+13r+36/r^2+17r+72*r^2+4r-32/r^2-13r+36

$$\frac { r ^ { 2 } + 13 r + 36 } { r ^ { 2 } + 17 r + 72 } \cdot \frac { r ^ { 2 } + 4 r - 32 } { r ^ { 2 } - 13 r + 36 }$$

Evaluate

$$\frac{r+4}{r-9}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{r^{2}+13r+36}{r^{2}+17r+72}.

$$\frac{\left(r+4\right)\left(r+9\right)}{\left(r+8\right)\left(r+9\right)}\times \frac{r^{2}+4r-32}{r^{2}-13r+36}$$

Cancel out r+9 in both numerator and denominator.

$$\frac{r+4}{r+8}\times \frac{r^{2}+4r-32}{r^{2}-13r+36}$$

Factor the expressions that are not already factored in \frac{r^{2}+4r-32}{r^{2}-13r+36}.

$$\frac{r+4}{r+8}\times \frac{\left(r-4\right)\left(r+8\right)}{\left(r-9\right)\left(r-4\right)}$$

Cancel out r-4 in both numerator and denominator.

$$\frac{r+4}{r+8}\times \frac{r+8}{r-9}$$

Multiply \frac{r+4}{r+8} times \frac{r+8}{r-9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(r+4\right)\left(r+8\right)}{\left(r+8\right)\left(r-9\right)}$$

Cancel out r+8 in both numerator and denominator.

$$\frac{r+4}{r-9}$$

Expand

$$\frac{r+4}{r-9}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{r^{2}+13r+36}{r^{2}+17r+72}.

$$\frac{\left(r+4\right)\left(r+9\right)}{\left(r+8\right)\left(r+9\right)}\times \frac{r^{2}+4r-32}{r^{2}-13r+36}$$

Cancel out r+9 in both numerator and denominator.

$$\frac{r+4}{r+8}\times \frac{r^{2}+4r-32}{r^{2}-13r+36}$$

Factor the expressions that are not already factored in \frac{r^{2}+4r-32}{r^{2}-13r+36}.

$$\frac{r+4}{r+8}\times \frac{\left(r-4\right)\left(r+8\right)}{\left(r-9\right)\left(r-4\right)}$$

Cancel out r-4 in both numerator and denominator.

$$\frac{r+4}{r+8}\times \frac{r+8}{r-9}$$

Multiply \frac{r+4}{r+8} times \frac{r+8}{r-9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(r+4\right)\left(r+8\right)}{\left(r+8\right)\left(r-9\right)}$$

Cancel out r+8 in both numerator and denominator.

$$\frac{r+4}{r-9}$$