Solve 9-6t+t^2/9-t^2*t^2-5t+6/3t^2-9t

$$\frac { 9 - 6 t + t ^ { 2 } } { 9 - t ^ { 2 } } \cdot \frac { t ^ { 2 } - 5 t + 6 } { 3 t ^ { 2 } - 9 t }$$

Evaluate

$$-\frac{\left(t-3\right)\left(t-2\right)}{3t\left(t+3\right)}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{9-6t+t^{2}}{9-t^{2}}.

$$\frac{\left(t-3\right)^{2}}{\left(t-3\right)\left(-t-3\right)}\times \frac{t^{2}-5t+6}{3t^{2}-9t}$$

Cancel out t-3 in both numerator and denominator.

$$\frac{t-3}{-t-3}\times \frac{t^{2}-5t+6}{3t^{2}-9t}$$

Factor the expressions that are not already factored in \frac{t^{2}-5t+6}{3t^{2}-9t}.

$$\frac{t-3}{-t-3}\times \frac{\left(t-3\right)\left(t-2\right)}{3t\left(t-3\right)}$$

Cancel out t-3 in both numerator and denominator.

$$\frac{t-3}{-t-3}\times \frac{t-2}{3t}$$

Multiply \frac{t-3}{-t-3} times \frac{t-2}{3t} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(t-3\right)\left(t-2\right)}{\left(-t-3\right)\times 3t}$$

Use the distributive property to multiply t-3 by t-2 and combine like terms.

$$\frac{t^{2}-5t+6}{\left(-t-3\right)\times 3t}$$

Use the distributive property to multiply -t-3 by 3.

$$\frac{t^{2}-5t+6}{\left(-3t-9\right)t}$$

Use the distributive property to multiply -3t-9 by t.

$$\frac{t^{2}-5t+6}{-3t^{2}-9t}$$

Expand

$$-\frac{t^{2}-5t+6}{3t\left(t+3\right)}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{9-6t+t^{2}}{9-t^{2}}.

$$\frac{\left(t-3\right)^{2}}{\left(t-3\right)\left(-t-3\right)}\times \frac{t^{2}-5t+6}{3t^{2}-9t}$$

Cancel out t-3 in both numerator and denominator.

$$\frac{t-3}{-t-3}\times \frac{t^{2}-5t+6}{3t^{2}-9t}$$

Factor the expressions that are not already factored in \frac{t^{2}-5t+6}{3t^{2}-9t}.

$$\frac{t-3}{-t-3}\times \frac{\left(t-3\right)\left(t-2\right)}{3t\left(t-3\right)}$$

Cancel out t-3 in both numerator and denominator.

$$\frac{t-3}{-t-3}\times \frac{t-2}{3t}$$

Multiply \frac{t-3}{-t-3} times \frac{t-2}{3t} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(t-3\right)\left(t-2\right)}{\left(-t-3\right)\times 3t}$$

Use the distributive property to multiply t-3 by t-2 and combine like terms.

$$\frac{t^{2}-5t+6}{\left(-t-3\right)\times 3t}$$

Use the distributive property to multiply -t-3 by 3.

$$\frac{t^{2}-5t+6}{\left(-3t-9\right)t}$$

Use the distributive property to multiply -3t-9 by t.

$$\frac{t^{2}-5t+6}{-3t^{2}-9t}$$