Solve 7v^2+35v/v+7*v^2+2v-35/v^2-25

$$\frac { 7 v ^ { 2 } + 35 v } { v + 7 } \cdot \frac { v ^ { 2 } + 2 v - 35 } { v ^ { 2 } - 25 }$$

Evaluate

$$7v$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{v^{2}+2v-35}{v^{2}-25}.

$$\frac{7v^{2}+35v}{v+7}\times \frac{\left(v-5\right)\left(v+7\right)}{\left(v-5\right)\left(v+5\right)}$$

Cancel out v-5 in both numerator and denominator.

$$\frac{7v^{2}+35v}{v+7}\times \frac{v+7}{v+5}$$

Multiply \frac{7v^{2}+35v}{v+7} times \frac{v+7}{v+5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(7v^{2}+35v\right)\left(v+7\right)}{\left(v+7\right)\left(v+5\right)}$$

Cancel out v+7 in both numerator and denominator.

$$\frac{7v^{2}+35v}{v+5}$$

Factor the expressions that are not already factored.

$$\frac{7v\left(v+5\right)}{v+5}$$

Cancel out v+5 in both numerator and denominator.

$$7v$$

Expand

$$7v$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{v^{2}+2v-35}{v^{2}-25}.

$$\frac{7v^{2}+35v}{v+7}\times \frac{\left(v-5\right)\left(v+7\right)}{\left(v-5\right)\left(v+5\right)}$$

Cancel out v-5 in both numerator and denominator.

$$\frac{7v^{2}+35v}{v+7}\times \frac{v+7}{v+5}$$

Multiply \frac{7v^{2}+35v}{v+7} times \frac{v+7}{v+5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(7v^{2}+35v\right)\left(v+7\right)}{\left(v+7\right)\left(v+5\right)}$$

Cancel out v+7 in both numerator and denominator.

$$\frac{7v^{2}+35v}{v+5}$$

Factor the expressions that are not already factored.

$$\frac{7v\left(v+5\right)}{v+5}$$

Cancel out v+5 in both numerator and denominator.

$$7v$$