Solve f(y)=y^2-36/3y+21*y+7/y-6

$$f ( y ) = \frac { y ^ { 2 } - 36 } { 3 y + 21 } \cdot \frac { y + 7 } { y - 6 }$$

Evaluate

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

Short Solution Steps

Multiply \frac{y^{2}-36}{3y+21} times \frac{y+7}{y-6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(y^{2}-36\right)\left(y+7\right)}{\left(3y+21\right)\left(y-6\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(y-6\right)\left(y+6\right)\left(y+7\right)}{3\left(y-6\right)\left(y+7\right)}$$

Cancel out \left(y-6\right)\left(y+7\right) in both numerator and denominator.

$$\frac{y+6}{3}$$

Expand

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

Short Solution Steps

Multiply \frac{y^{2}-36}{3y+21} times \frac{y+7}{y-6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(y^{2}-36\right)\left(y+7\right)}{\left(3y+21\right)\left(y-6\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(y-6\right)\left(y+6\right)\left(y+7\right)}{3\left(y-6\right)\left(y+7\right)}$$

Cancel out \left(y-6\right)\left(y+7\right) in both numerator and denominator.

$$\frac{y+6}{3}$$