Solve y+6/(y+1)(y+2)*y+1/y+6

$$\frac { y + 6 } { ( y + 1 ) ( y + 2 ) } \times \frac { y + 1 } { y + 6 }$$

Evaluate

$$\frac{1}{y+2}$$

Short Solution Steps

Apply the distributive property by multiplying each term of y+1 by each term of y+2.

$$\frac{y+6}{y^{2}+2y+y+2}\times \frac{y+1}{y+6}$$

Combine 2y and y to get 3y.

$$\frac{y+6}{y^{2}+3y+2}\times \frac{y+1}{y+6}$$

Multiply \frac{y+6}{y^{2}+3y+2} times \frac{y+1}{y+6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(y+6\right)\left(y+1\right)}{\left(y^{2}+3y+2\right)\left(y+6\right)}$$

Cancel out y+6 in both numerator and denominator.

$$\frac{y+1}{y^{2}+3y+2}$$

Factor the expressions that are not already factored.

$$\frac{y+1}{\left(y+1\right)\left(y+2\right)}$$

Cancel out y+1 in both numerator and denominator.

$$\frac{1}{y+2}$$

Expand

$$\frac{1}{y+2}$$

Short Solution Steps

Apply the distributive property by multiplying each term of y+1 by each term of y+2.

$$\frac{y+6}{y^{2}+2y+y+2}\times \frac{y+1}{y+6}$$

Combine 2y and y to get 3y.

$$\frac{y+6}{y^{2}+3y+2}\times \frac{y+1}{y+6}$$

Multiply \frac{y+6}{y^{2}+3y+2} times \frac{y+1}{y+6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(y+6\right)\left(y+1\right)}{\left(y^{2}+3y+2\right)\left(y+6\right)}$$

Cancel out y+6 in both numerator and denominator.

$$\frac{y+1}{y^{2}+3y+2}$$

Factor the expressions that are not already factored.

$$\frac{y+1}{\left(y+1\right)\left(y+2\right)}$$

Cancel out y+1 in both numerator and denominator.

$$\frac{1}{y+2}$$