Solve (2left(1-x/8right)+2left(1-x/24right))(1/2(1+x/24))

$$(2 \left( 1- \frac{ x }{ 8 } \right) +2 \left( 1- \frac{ x }{ 24 } \right) )( \frac{ 1 }{ 2 } (1+ \frac{ x }{ 24 } ))$$

Evaluate

$$-\frac{x^{2}}{144}-\frac{x}{12}+2$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{8}{8}.

$$\left(2\left(\frac{8}{8}-\frac{x}{8}\right)+2\left(1-\frac{x}{24}\right)\right)\times \frac{1}{2}\left(1+\frac{x}{24}\right)$$

Since \frac{8}{8} and \frac{x}{8} have the same denominator, subtract them by subtracting their numerators.

$$\left(2\times \frac{8-x}{8}+2\left(1-\frac{x}{24}\right)\right)\times \frac{1}{2}\left(1+\frac{x}{24}\right)$$

Cancel out 8, the greatest common factor in 2 and 8.

$$\left(\frac{8-x}{4}+2\left(1-\frac{x}{24}\right)\right)\times \frac{1}{2}\left(1+\frac{x}{24}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{24}{24}.

$$\left(\frac{8-x}{4}+2\left(\frac{24}{24}-\frac{x}{24}\right)\right)\times \frac{1}{2}\left(1+\frac{x}{24}\right)$$

Since \frac{24}{24} and \frac{x}{24} have the same denominator, subtract them by subtracting their numerators.

$$\left(\frac{8-x}{4}+2\times \frac{24-x}{24}\right)\times \frac{1}{2}\left(1+\frac{x}{24}\right)$$

Cancel out 24, the greatest common factor in 2 and 24.

$$\left(\frac{8-x}{4}+\frac{24-x}{12}\right)\times \frac{1}{2}\left(1+\frac{x}{24}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 12 is 12. Multiply \frac{8-x}{4} times \frac{3}{3}.

$$\left(\frac{3\left(8-x\right)}{12}+\frac{24-x}{12}\right)\times \frac{1}{2}\left(1+\frac{x}{24}\right)$$

Since \frac{3\left(8-x\right)}{12} and \frac{24-x}{12} have the same denominator, add them by adding their numerators.

$$\frac{3\left(8-x\right)+24-x}{12}\times \frac{1}{2}\left(1+\frac{x}{24}\right)$$

Do the multiplications in 3\left(8-x\right)+24-x.

$$\frac{24-3x+24-x}{12}\times \frac{1}{2}\left(1+\frac{x}{24}\right)$$

Combine like terms in 24-3x+24-x.

$$\frac{48-4x}{12}\times \frac{1}{2}\left(1+\frac{x}{24}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{24}{24}.

$$\frac{48-4x}{12}\times \frac{1}{2}\left(\frac{24}{24}+\frac{x}{24}\right)$$

Since \frac{24}{24} and \frac{x}{24} have the same denominator, add them by adding their numerators.

$$\frac{48-4x}{12}\times \frac{1}{2}\times \frac{24+x}{24}$$

Multiply \frac{48-4x}{12} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{48-4x}{12\times 2}\times \frac{24+x}{24}$$

Multiply \frac{48-4x}{12\times 2} times \frac{24+x}{24} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(48-4x\right)\left(24+x\right)}{12\times 2\times 24}$$

Multiply 12 and 2 to get 24.

$$\frac{\left(48-4x\right)\left(24+x\right)}{24\times 24}$$

Multiply 24 and 24 to get 576.

$$\frac{\left(48-4x\right)\left(24+x\right)}{576}$$

Apply the distributive property by multiplying each term of 48-4x by each term of 24+x.

$$\frac{1152+48x-96x-4x^{2}}{576}$$

Combine 48x and -96x to get -48x.

$$\frac{1152-48x-4x^{2}}{576}$$

Expand

$$-\frac{x^{2}}{144}-\frac{x}{12}+2$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{8}{8}.

$$\left(2\left(\frac{8}{8}-\frac{x}{8}\right)+2\left(1-\frac{x}{24}\right)\right)\times \frac{1}{2}\left(1+\frac{x}{24}\right)$$

Since \frac{8}{8} and \frac{x}{8} have the same denominator, subtract them by subtracting their numerators.

$$\left(2\times \frac{8-x}{8}+2\left(1-\frac{x}{24}\right)\right)\times \frac{1}{2}\left(1+\frac{x}{24}\right)$$

Cancel out 8, the greatest common factor in 2 and 8.

$$\left(\frac{8-x}{4}+2\left(1-\frac{x}{24}\right)\right)\times \frac{1}{2}\left(1+\frac{x}{24}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{24}{24}.

$$\left(\frac{8-x}{4}+2\left(\frac{24}{24}-\frac{x}{24}\right)\right)\times \frac{1}{2}\left(1+\frac{x}{24}\right)$$

Since \frac{24}{24} and \frac{x}{24} have the same denominator, subtract them by subtracting their numerators.

$$\left(\frac{8-x}{4}+2\times \frac{24-x}{24}\right)\times \frac{1}{2}\left(1+\frac{x}{24}\right)$$

Cancel out 24, the greatest common factor in 2 and 24.

$$\left(\frac{8-x}{4}+\frac{24-x}{12}\right)\times \frac{1}{2}\left(1+\frac{x}{24}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 12 is 12. Multiply \frac{8-x}{4} times \frac{3}{3}.

$$\left(\frac{3\left(8-x\right)}{12}+\frac{24-x}{12}\right)\times \frac{1}{2}\left(1+\frac{x}{24}\right)$$

Since \frac{3\left(8-x\right)}{12} and \frac{24-x}{12} have the same denominator, add them by adding their numerators.

$$\frac{3\left(8-x\right)+24-x}{12}\times \frac{1}{2}\left(1+\frac{x}{24}\right)$$

Do the multiplications in 3\left(8-x\right)+24-x.

$$\frac{24-3x+24-x}{12}\times \frac{1}{2}\left(1+\frac{x}{24}\right)$$

Combine like terms in 24-3x+24-x.

$$\frac{48-4x}{12}\times \frac{1}{2}\left(1+\frac{x}{24}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{24}{24}.

$$\frac{48-4x}{12}\times \frac{1}{2}\left(\frac{24}{24}+\frac{x}{24}\right)$$

Since \frac{24}{24} and \frac{x}{24} have the same denominator, add them by adding their numerators.

$$\frac{48-4x}{12}\times \frac{1}{2}\times \frac{24+x}{24}$$

Multiply \frac{48-4x}{12} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{48-4x}{12\times 2}\times \frac{24+x}{24}$$

Multiply \frac{48-4x}{12\times 2} times \frac{24+x}{24} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(48-4x\right)\left(24+x\right)}{12\times 2\times 24}$$

Multiply 12 and 2 to get 24.

$$\frac{\left(48-4x\right)\left(24+x\right)}{24\times 24}$$

Multiply 24 and 24 to get 576.

$$\frac{\left(48-4x\right)\left(24+x\right)}{576}$$

Apply the distributive property by multiplying each term of 48-4x by each term of 24+x.

$$\frac{1152+48x-96x-4x^{2}}{576}$$

Combine 48x and -96x to get -48x.

$$\frac{1152-48x-4x^{2}}{576}$$