Solve 5/9-24t^3*3t-2/3t^2div5t-2

$$\frac { 5 } { 9 - 24 t ^ { 3 } } \cdot \frac { 3 t - 2 } { 3 t ^ { 2 } \div 5 t - 2 }$$

Evaluate

$$\frac{25\left(3t-2\right)}{3\left(3-8t^{3}\right)\left(3t^{3}-10\right)}$$

Short Solution Steps

Express \frac{3t^{2}}{5}t as a single fraction.

$$\frac{5}{9-24t^{3}}\times \frac{3t-2}{\frac{3t^{2}t}{5}-2}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{5}{5}.

$$\frac{5}{9-24t^{3}}\times \frac{3t-2}{\frac{3t^{2}t}{5}-\frac{2\times 5}{5}}$$

Since \frac{3t^{2}t}{5} and \frac{2\times 5}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{9-24t^{3}}\times \frac{3t-2}{\frac{3t^{2}t-2\times 5}{5}}$$

Do the multiplications in 3t^{2}t-2\times 5.

$$\frac{5}{9-24t^{3}}\times \frac{3t-2}{\frac{3t^{3}-10}{5}}$$

Divide 3t-2 by \frac{3t^{3}-10}{5} by multiplying 3t-2 by the reciprocal of \frac{3t^{3}-10}{5}.

$$\frac{5}{9-24t^{3}}\times \frac{\left(3t-2\right)\times 5}{3t^{3}-10}$$

Multiply \frac{5}{9-24t^{3}} times \frac{\left(3t-2\right)\times 5}{3t^{3}-10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\left(3t-2\right)\times 5}{\left(9-24t^{3}\right)\left(3t^{3}-10\right)}$$

Multiply 5 and 5 to get 25.

$$\frac{25\left(3t-2\right)}{\left(9-24t^{3}\right)\left(3t^{3}-10\right)}$$

Use the distributive property to multiply 25 by 3t-2.

$$\frac{75t-50}{\left(9-24t^{3}\right)\left(3t^{3}-10\right)}$$

Use the distributive property to multiply 9-24t^{3} by 3t^{3}-10 and combine like terms.

$$\frac{75t-50}{267t^{3}-90-72t^{6}}$$

Expand

$$-\frac{25\left(3t-2\right)}{3\left(3t^{3}-10\right)\left(8t^{3}-3\right)}$$

Short Solution Steps

Express \frac{3t^{2}}{5}t as a single fraction.

$$\frac{5}{9-24t^{3}}\times \frac{3t-2}{\frac{3t^{2}t}{5}-2}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{5}{5}.

$$\frac{5}{9-24t^{3}}\times \frac{3t-2}{\frac{3t^{2}t}{5}-\frac{2\times 5}{5}}$$

Since \frac{3t^{2}t}{5} and \frac{2\times 5}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{9-24t^{3}}\times \frac{3t-2}{\frac{3t^{2}t-2\times 5}{5}}$$

Do the multiplications in 3t^{2}t-2\times 5.

$$\frac{5}{9-24t^{3}}\times \frac{3t-2}{\frac{3t^{3}-10}{5}}$$

Divide 3t-2 by \frac{3t^{3}-10}{5} by multiplying 3t-2 by the reciprocal of \frac{3t^{3}-10}{5}.

$$\frac{5}{9-24t^{3}}\times \frac{\left(3t-2\right)\times 5}{3t^{3}-10}$$

Multiply \frac{5}{9-24t^{3}} times \frac{\left(3t-2\right)\times 5}{3t^{3}-10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\left(3t-2\right)\times 5}{\left(9-24t^{3}\right)\left(3t^{3}-10\right)}$$

Multiply 5 and 5 to get 25.

$$\frac{25\left(3t-2\right)}{\left(9-24t^{3}\right)\left(3t^{3}-10\right)}$$

Use the distributive property to multiply 25 by 3t-2.

$$\frac{75t-50}{\left(9-24t^{3}\right)\left(3t^{3}-10\right)}$$

Use the distributive property to multiply 9-24t^{3} by 3t^{3}-10 and combine like terms.

$$\frac{75t-50}{267t^{3}-90-72t^{6}}$$