Solve 48left(p-24right)6/55564/p

$$48 \left( p-24 \right) \frac{ 6 }{ 5 } \frac{ 5564 }{ p }$$

Evaluate

$$\frac{1602432}{5}-\frac{38458368}{5p}$$

Short Solution Steps

Express 48\times \frac{6}{5} as a single fraction.

$$\frac{48\times 6}{5}\left(p-24\right)\times \frac{5564}{p}$$

Multiply 48 and 6 to get 288.

$$\frac{288}{5}\left(p-24\right)\times \frac{5564}{p}$$

Multiply \frac{288}{5} times \frac{5564}{p} by multiplying numerator times numerator and denominator times denominator.

$$\frac{288\times 5564}{5p}\left(p-24\right)$$

Use the distributive property to multiply \frac{288\times 5564}{5p} by p-24.

$$\frac{288\times 5564}{5p}p-24\times \frac{288\times 5564}{5p}$$

Multiply 288 and 5564 to get 1602432.

$$\frac{1602432}{5p}p-24\times \frac{288\times 5564}{5p}$$

Express \frac{1602432}{5p}p as a single fraction.

$$\frac{1602432p}{5p}-24\times \frac{288\times 5564}{5p}$$

Cancel out p in both numerator and denominator.

$$\frac{1602432}{5}-24\times \frac{288\times 5564}{5p}$$

Multiply 288 and 5564 to get 1602432.

$$\frac{1602432}{5}-24\times \frac{1602432}{5p}$$

Express -24\times \frac{1602432}{5p} as a single fraction.

$$\frac{1602432}{5}+\frac{-24\times 1602432}{5p}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5 and 5p is 5p. Multiply \frac{1602432}{5} times \frac{p}{p}.

$$\frac{1602432p}{5p}+\frac{-24\times 1602432}{5p}$$

Since \frac{1602432p}{5p} and \frac{-24\times 1602432}{5p} have the same denominator, add them by adding their numerators.

$$\frac{1602432p-24\times 1602432}{5p}$$

Do the multiplications in 1602432p-24\times 1602432.

$$\frac{1602432p-38458368}{5p}$$

Expand

$$\frac{1602432}{5}-\frac{38458368}{5p}$$

Short Solution Steps

Express 48\times \frac{6}{5} as a single fraction.

$$\frac{48\times 6}{5}\left(p-24\right)\times \frac{5564}{p}$$

Multiply 48 and 6 to get 288.

$$\frac{288}{5}\left(p-24\right)\times \frac{5564}{p}$$

Multiply \frac{288}{5} times \frac{5564}{p} by multiplying numerator times numerator and denominator times denominator.

$$\frac{288\times 5564}{5p}\left(p-24\right)$$

Use the distributive property to multiply \frac{288\times 5564}{5p} by p-24.

$$\frac{288\times 5564}{5p}p-24\times \frac{288\times 5564}{5p}$$

Multiply 288 and 5564 to get 1602432.

$$\frac{1602432}{5p}p-24\times \frac{288\times 5564}{5p}$$

Express \frac{1602432}{5p}p as a single fraction.

$$\frac{1602432p}{5p}-24\times \frac{288\times 5564}{5p}$$

Cancel out p in both numerator and denominator.

$$\frac{1602432}{5}-24\times \frac{288\times 5564}{5p}$$

Multiply 288 and 5564 to get 1602432.

$$\frac{1602432}{5}-24\times \frac{1602432}{5p}$$

Express -24\times \frac{1602432}{5p} as a single fraction.

$$\frac{1602432}{5}+\frac{-24\times 1602432}{5p}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5 and 5p is 5p. Multiply \frac{1602432}{5} times \frac{p}{p}.

$$\frac{1602432p}{5p}+\frac{-24\times 1602432}{5p}$$

Since \frac{1602432p}{5p} and \frac{-24\times 1602432}{5p} have the same denominator, add them by adding their numerators.

$$\frac{1602432p-24\times 1602432}{5p}$$

Do the multiplications in 1602432p-24\times 1602432.

$$\frac{1602432p-38458368}{5p}$$