Solve frac{3a^{2}}{5y}:frac{9a^{3}}{15y^2}=3a^2*15y^2/5y*9a^3=y/a

$$\frac { 3 a ^ { 2 } } { 5 y } : \frac { 9 a ^ { 3 } } { 15 y ^ { 2 } } = \frac { 3 a ^ { 2 } \cdot 15 y ^ { 2 } } { 5 y \cdot 9 a ^ { 3 } } = \frac { y } { a }$$

Evaluate (complex solution)

Solution Steps

Divide \frac{3a^{2}}{5y} by \frac{9a^{3}}{15y^{2}} by multiplying \frac{3a^{2}}{5y} by the reciprocal of \frac{9a^{3}}{15y^{2}}.

$$\frac{3a^{2}\times 15y^{2}}{5y\times 9a^{3}}=\frac{3a^{2}\times 15y^{2}}{5y\times 9a^{3}}\text{ and }\frac{3a^{2}\times 15y^{2}}{5y\times 9a^{3}}=\frac{y}{a}$$

Cancel out 3\times 3\times 5ya^{2} in both numerator and denominator.

$$\frac{y}{a}=\frac{3a^{2}\times 15y^{2}}{5y\times 9a^{3}}\text{ and }\frac{3a^{2}\times 15y^{2}}{5y\times 9a^{3}}=\frac{y}{a}$$

Cancel out 3\times 3\times 5ya^{2} in both numerator and denominator.

$$\frac{y}{a}=\frac{y}{a}\text{ and }\frac{3a^{2}\times 15y^{2}}{5y\times 9a^{3}}=\frac{y}{a}$$

Cancel out 3\times 3\times 5ya^{2} in both numerator and denominator.

$$\frac{y}{a}=\frac{y}{a}\text{ and }\frac{y}{a}=\frac{y}{a}$$

Subtract \frac{y}{a} from both sides.

$$\frac{y}{a}-\frac{y}{a}=0\text{ and }\frac{y}{a}=\frac{y}{a}$$

Subtract \frac{y}{a} from \frac{y}{a} to get 0.

$$0=0\text{ and }\frac{y}{a}=\frac{y}{a}$$

Compare 0 and 0.

$$\text{true}\text{ and }\frac{y}{a}=\frac{y}{a}$$

Subtract \frac{y}{a} from both sides.

$$\text{true}\text{ and }\frac{y}{a}-\frac{y}{a}=0$$

Subtract \frac{y}{a} from \frac{y}{a} to get 0.

$$\text{true}\text{ and }0=0$$

Compare 0 and 0.

$$\text{true}\text{ and }\text{true}$$

The conjunction of \text{true} and \text{true} is \text{true}.

$$\text{true}$$

Solve for y

$$y\neq 0$$

$$a\neq 0$$

Solve for a

$$a\neq 0$$

$$y\neq 0$$