Solve y-5/v+2*2+y/5-v

$$\frac { y - 5 } { v + 2 } \cdot \frac { 2 + y } { 5 - v }$$

Evaluate

$$\frac{\left(y-5\right)\left(y+2\right)}{\left(5-v\right)\left(v+2\right)}$$

Short Solution Steps

Multiply \frac{y-5}{v+2} times \frac{2+y}{5-v} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(y-5\right)\left(2+y\right)}{\left(v+2\right)\left(5-v\right)}$$

Apply the distributive property by multiplying each term of y-5 by each term of 2+y.

$$\frac{2y+y^{2}-10-5y}{\left(v+2\right)\left(5-v\right)}$$

Combine 2y and -5y to get -3y.

$$\frac{-3y+y^{2}-10}{\left(v+2\right)\left(5-v\right)}$$

Apply the distributive property by multiplying each term of v+2 by each term of 5-v.

$$\frac{-3y+y^{2}-10}{5v-v^{2}+10-2v}$$

Combine 5v and -2v to get 3v.

$$\frac{-3y+y^{2}-10}{3v-v^{2}+10}$$

Expand

$$\frac{y^{2}-3y-10}{\left(5-v\right)\left(v+2\right)}$$

Short Solution Steps

Multiply \frac{y-5}{v+2} times \frac{2+y}{5-v} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(y-5\right)\left(2+y\right)}{\left(v+2\right)\left(5-v\right)}$$

Apply the distributive property by multiplying each term of y-5 by each term of 2+y.

$$\frac{2y+y^{2}-10-5y}{\left(v+2\right)\left(5-v\right)}$$

Combine 2y and -5y to get -3y.

$$\frac{-3y+y^{2}-10}{\left(v+2\right)\left(5-v\right)}$$

Apply the distributive property by multiplying each term of v+2 by each term of 5-v.

$$\frac{-3y+y^{2}-10}{5v-v^{2}+10-2v}$$

Combine 5v and -2v to get 3v.

$$\frac{-3y+y^{2}-10}{3v-v^{2}+10}$$