Solve w^2-81/4w^2+27w-7*w^2-5w-36/w^2+11w+28

$$\frac { w ^ { 2 } - 81 } { 4 w ^ { 2 } + 27 w - 7 } \cdot \frac { w ^ { 2 } - 5 w - 36 } { w ^ { 2 } + 11 w + 28 }$$

Evaluate

$$\frac{\left(\frac{w-9}{w+7}\right)^{2}\left(w+9\right)}{4w-1}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{w^{2}-5w-36}{w^{2}+11w+28}.

$$\frac{w^{2}-81}{4w^{2}+27w-7}\times \frac{\left(w-9\right)\left(w+4\right)}{\left(w+4\right)\left(w+7\right)}$$

Cancel out w+4 in both numerator and denominator.

$$\frac{w^{2}-81}{4w^{2}+27w-7}\times \frac{w-9}{w+7}$$

Multiply \frac{w^{2}-81}{4w^{2}+27w-7} times \frac{w-9}{w+7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(w^{2}-81\right)\left(w-9\right)}{\left(4w^{2}+27w-7\right)\left(w+7\right)}$$

Use the distributive property to multiply w^{2}-81 by w-9.

$$\frac{w^{3}-9w^{2}-81w+729}{\left(4w^{2}+27w-7\right)\left(w+7\right)}$$

Use the distributive property to multiply 4w^{2}+27w-7 by w+7 and combine like terms.

$$\frac{w^{3}-9w^{2}-81w+729}{4w^{3}+55w^{2}+182w-49}$$

Expand

$$\frac{w^{3}-9w^{2}-81w+729}{\left(w+7\right)\left(4w^{2}+27w-7\right)}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{w^{2}-5w-36}{w^{2}+11w+28}.

$$\frac{w^{2}-81}{4w^{2}+27w-7}\times \frac{\left(w-9\right)\left(w+4\right)}{\left(w+4\right)\left(w+7\right)}$$

Cancel out w+4 in both numerator and denominator.

$$\frac{w^{2}-81}{4w^{2}+27w-7}\times \frac{w-9}{w+7}$$

Multiply \frac{w^{2}-81}{4w^{2}+27w-7} times \frac{w-9}{w+7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(w^{2}-81\right)\left(w-9\right)}{\left(4w^{2}+27w-7\right)\left(w+7\right)}$$

Use the distributive property to multiply w^{2}-81 by w-9.

$$\frac{w^{3}-9w^{2}-81w+729}{\left(4w^{2}+27w-7\right)\left(w+7\right)}$$

Use the distributive property to multiply 4w^{2}+27w-7 by w+7 and combine like terms.

$$\frac{w^{3}-9w^{2}-81w+729}{4w^{3}+55w^{2}+182w-49}$$