Solve 18(y-6)^3(2y-3)^3/30(2y-3)^4(y-6)^4

$$\frac { 18 ( y - 6 ) ^ { 3 } ( 2 y - 3 ) ^ { 3 } } { 30 ( 2 y - 3 ) ^ { 4 } ( y - 6 ) ^ { 4 } }$$

Evaluate

$$\frac{3}{5\left(y-6\right)\left(2y-3\right)}$$

Solution Steps

Cancel out 6\left(y-6\right)^{3}\left(2y-3\right)^{3} in both numerator and denominator.

$$\frac{3}{5\left(y-6\right)\left(2y-3\right)}$$

Use the distributive property to multiply 5 by y-6.

$$\frac{3}{\left(5y-30\right)\left(2y-3\right)}$$

Use the distributive property to multiply 5y-30 by 2y-3 and combine like terms.

$$\frac{3}{10y^{2}-75y+90}$$

Expand

$$\frac{3}{5\left(y-6\right)\left(2y-3\right)}$$

Solution Steps

Cancel out 6\left(y-6\right)^{3}\left(2y-3\right)^{3} in both numerator and denominator.

$$\frac{3}{5\left(y-6\right)\left(2y-3\right)}$$

Use the distributive property to multiply 5 by y-6.

$$\frac{3}{\left(5y-30\right)\left(2y-3\right)}$$

Use the distributive property to multiply 5y-30 by 2y-3 and combine like terms.

$$\frac{3}{10y^{2}-75y+90}$$