Solve (v+5)^3/(v+4)^3*v^2+8v+16/v^2+10v+25

$$\frac { ( v + 5 ) ^ { 3 } } { ( v + 4 ) ^ { 3 } } \cdot \frac { v ^ { 2 } + 8 v + 16 } { v ^ { 2 } + 10 v + 25 }$$

Evaluate

$$\frac{v+5}{v+4}$$

Short Solution Steps

Multiply \frac{\left(v+5\right)^{3}}{\left(v+4\right)^{3}} times \frac{v^{2}+8v+16}{v^{2}+10v+25} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(v+5\right)^{3}\left(v^{2}+8v+16\right)}{\left(v+4\right)^{3}\left(v^{2}+10v+25\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(v+4\right)^{2}\left(v+5\right)^{3}}{\left(v+5\right)^{2}\left(v+4\right)^{3}}$$

Cancel out \left(v+4\right)^{2}\left(v+5\right)^{2} in both numerator and denominator.

$$\frac{v+5}{v+4}$$

Expand

$$\frac{v+5}{v+4}$$

Short Solution Steps

Multiply \frac{\left(v+5\right)^{3}}{\left(v+4\right)^{3}} times \frac{v^{2}+8v+16}{v^{2}+10v+25} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(v+5\right)^{3}\left(v^{2}+8v+16\right)}{\left(v+4\right)^{3}\left(v^{2}+10v+25\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(v+4\right)^{2}\left(v+5\right)^{3}}{\left(v+5\right)^{2}\left(v+4\right)^{3}}$$

Cancel out \left(v+4\right)^{2}\left(v+5\right)^{2} in both numerator and denominator.

$$\frac{v+5}{v+4}$$