Solve (y+4)^3/(y+9)^3*y^2+18y+81/y^2+8y+16

$$\frac { ( y + 4 ) ^ { 3 } } { ( y + 9 ) ^ { 3 } } \cdot \frac { y ^ { 2 } + 18 y + 81 } { y ^ { 2 } + 8 y + 16 }$$

Evaluate

$$\frac{y+4}{y+9}$$

Short Solution Steps

Multiply \frac{\left(y+4\right)^{3}}{\left(y+9\right)^{3}} times \frac{y^{2}+18y+81}{y^{2}+8y+16} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(y+4\right)^{3}\left(y^{2}+18y+81\right)}{\left(y+9\right)^{3}\left(y^{2}+8y+16\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(y+9\right)^{2}\left(y+4\right)^{3}}{\left(y+4\right)^{2}\left(y+9\right)^{3}}$$

Cancel out \left(y+4\right)^{2}\left(y+9\right)^{2} in both numerator and denominator.

$$\frac{y+4}{y+9}$$

Expand

$$\frac{y+4}{y+9}$$

Short Solution Steps

Multiply \frac{\left(y+4\right)^{3}}{\left(y+9\right)^{3}} times \frac{y^{2}+18y+81}{y^{2}+8y+16} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(y+4\right)^{3}\left(y^{2}+18y+81\right)}{\left(y+9\right)^{3}\left(y^{2}+8y+16\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(y+9\right)^{2}\left(y+4\right)^{3}}{\left(y+4\right)^{2}\left(y+9\right)^{3}}$$

Cancel out \left(y+4\right)^{2}\left(y+9\right)^{2} in both numerator and denominator.

$$\frac{y+4}{y+9}$$