Solve (x/3-3/x)(x/4+4/x)

$$( \frac { x } { 3 } - \frac { 3 } { x } ) ( \frac { x } { 4 } + \frac { 4 } { x } )$$

Evaluate

$$\frac{x^{2}}{12}+\frac{7}{12}-\frac{12}{x^{2}}$$

Short Solution Steps

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

$$\left(\frac{xx}{3x}-\frac{3\times 3}{3x}\right)\left(\frac{x}{4}+\frac{4}{x}\right)$$

Since \frac{xx}{3x} and \frac{3\times 3}{3x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{xx-3\times 3}{3x}\left(\frac{x}{4}+\frac{4}{x}\right)$$

Do the multiplications in xx-3\times 3.

$$\frac{x^{2}-9}{3x}\left(\frac{x}{4}+\frac{4}{x}\right)$$

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

$$\frac{x^{2}-9}{3x}\left(\frac{xx}{4x}+\frac{4\times 4}{4x}\right)$$

Since \frac{xx}{4x} and \frac{4\times 4}{4x} have the same denominator, add them by adding their numerators.

$$\frac{x^{2}-9}{3x}\times \frac{xx+4\times 4}{4x}$$

Do the multiplications in xx+4\times 4.

$$\frac{x^{2}-9}{3x}\times \frac{x^{2}+16}{4x}$$

Multiply \frac{x^{2}-9}{3x} times \frac{x^{2}+16}{4x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x^{2}-9\right)\left(x^{2}+16\right)}{3x\times 4x}$$

Multiply x and x to get x^{2}.

$$\frac{\left(x^{2}-9\right)\left(x^{2}+16\right)}{3x^{2}\times 4}$$

Multiply 3 and 4 to get 12.

$$\frac{\left(x^{2}-9\right)\left(x^{2}+16\right)}{12x^{2}}$$

Apply the distributive property by multiplying each term of x^{2}-9 by each term of x^{2}+16.

$$\frac{x^{4}+16x^{2}-9x^{2}-144}{12x^{2}}$$

Combine 16x^{2} and -9x^{2} to get 7x^{2}.

$$\frac{x^{4}+7x^{2}-144}{12x^{2}}$$

Expand

$$\frac{x^{2}}{12}+\frac{7}{12}-\frac{12}{x^{2}}$$

Short Solution Steps

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

$$\left(\frac{xx}{3x}-\frac{3\times 3}{3x}\right)\left(\frac{x}{4}+\frac{4}{x}\right)$$

Since \frac{xx}{3x} and \frac{3\times 3}{3x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{xx-3\times 3}{3x}\left(\frac{x}{4}+\frac{4}{x}\right)$$

Do the multiplications in xx-3\times 3.

$$\frac{x^{2}-9}{3x}\left(\frac{x}{4}+\frac{4}{x}\right)$$

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

$$\frac{x^{2}-9}{3x}\left(\frac{xx}{4x}+\frac{4\times 4}{4x}\right)$$

Since \frac{xx}{4x} and \frac{4\times 4}{4x} have the same denominator, add them by adding their numerators.

$$\frac{x^{2}-9}{3x}\times \frac{xx+4\times 4}{4x}$$

Do the multiplications in xx+4\times 4.

$$\frac{x^{2}-9}{3x}\times \frac{x^{2}+16}{4x}$$

Multiply \frac{x^{2}-9}{3x} times \frac{x^{2}+16}{4x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x^{2}-9\right)\left(x^{2}+16\right)}{3x\times 4x}$$

Multiply x and x to get x^{2}.

$$\frac{\left(x^{2}-9\right)\left(x^{2}+16\right)}{3x^{2}\times 4}$$

Multiply 3 and 4 to get 12.

$$\frac{\left(x^{2}-9\right)\left(x^{2}+16\right)}{12x^{2}}$$

Apply the distributive property by multiplying each term of x^{2}-9 by each term of x^{2}+16.

$$\frac{x^{4}+16x^{2}-9x^{2}-144}{12x^{2}}$$

Combine 16x^{2} and -9x^{2} to get 7x^{2}.

$$\frac{x^{4}+7x^{2}-144}{12x^{2}}$$