Solve (y^2-36)+y+6/y-4

$$( y ^ { 2 } - 36 ) + \frac { y + 6 } { y - 4 }$$

Evaluate

$$\frac{\left(y+6\right)\left(y-5\right)^{2}}{y-4}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply y^{2}-36 times \frac{y-4}{y-4}.

$$\frac{\left(y^{2}-36\right)\left(y-4\right)}{y-4}+\frac{y+6}{y-4}$$

Since \frac{\left(y^{2}-36\right)\left(y-4\right)}{y-4} and \frac{y+6}{y-4} have the same denominator, add them by adding their numerators.

$$\frac{\left(y^{2}-36\right)\left(y-4\right)+y+6}{y-4}$$

Do the multiplications in \left(y^{2}-36\right)\left(y-4\right)+y+6.

$$\frac{y^{3}-4y^{2}-36y+144+y+6}{y-4}$$

Combine like terms in y^{3}-4y^{2}-36y+144+y+6.

$$\frac{y^{3}-4y^{2}-35y+150}{y-4}$$

Expand

$$\frac{y^{3}-4y^{2}-35y+150}{y-4}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply y^{2}-36 times \frac{y-4}{y-4}.

$$\frac{\left(y^{2}-36\right)\left(y-4\right)}{y-4}+\frac{y+6}{y-4}$$

Since \frac{\left(y^{2}-36\right)\left(y-4\right)}{y-4} and \frac{y+6}{y-4} have the same denominator, add them by adding their numerators.

$$\frac{\left(y^{2}-36\right)\left(y-4\right)+y+6}{y-4}$$

Do the multiplications in \left(y^{2}-36\right)\left(y-4\right)+y+6.

$$\frac{y^{3}-4y^{2}-36y+144+y+6}{y-4}$$

Combine like terms in y^{3}-4y^{2}-36y+144+y+6.

$$\frac{y^{3}-4y^{2}-35y+150}{y-4}$$