Solve (1/x-3)(3/x+1)

$$( \frac { 1 } { x } - 3 ) ( \frac { 3 } { x } + 1 )$$

Evaluate

$$\frac{\left(1-3x\right)\left(x+3\right)}{x^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{x}{x}.

$$\left(\frac{1}{x}-\frac{3x}{x}\right)\left(\frac{3}{x}+1\right)$$

Since \frac{1}{x} and \frac{3x}{x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1-3x}{x}\left(\frac{3}{x}+1\right)$$

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

$$\frac{1-3x}{x}\left(\frac{3}{x}+\frac{x}{x}\right)$$

Since \frac{3}{x} and \frac{x}{x} have the same denominator, add them by adding their numerators.

$$\frac{1-3x}{x}\times \frac{3+x}{x}$$

Multiply \frac{1-3x}{x} times \frac{3+x}{x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(1-3x\right)\left(3+x\right)}{xx}$$

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

$$\frac{\left(1-3x\right)\left(3+x\right)}{x^{2}}$$

Apply the distributive property by multiplying each term of 1-3x by each term of 3+x.

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

Combine x and -9x to get -8x.

$$\frac{3-8x-3x^{2}}{x^{2}}$$

Expand

$$-3-\frac{8}{x}+\frac{3}{x^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{x}{x}.

$$\left(\frac{1}{x}-\frac{3x}{x}\right)\left(\frac{3}{x}+1\right)$$

Since \frac{1}{x} and \frac{3x}{x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1-3x}{x}\left(\frac{3}{x}+1\right)$$

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

$$\frac{1-3x}{x}\left(\frac{3}{x}+\frac{x}{x}\right)$$

Since \frac{3}{x} and \frac{x}{x} have the same denominator, add them by adding their numerators.

$$\frac{1-3x}{x}\times \frac{3+x}{x}$$

Multiply \frac{1-3x}{x} times \frac{3+x}{x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(1-3x\right)\left(3+x\right)}{xx}$$

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

$$\frac{\left(1-3x\right)\left(3+x\right)}{x^{2}}$$

Apply the distributive property by multiplying each term of 1-3x by each term of 3+x.

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

Combine x and -9x to get -8x.

$$\frac{3-8x-3x^{2}}{x^{2}}$$