Solve 1(x+1-3/5-1)*x-1/x-2

$$1 ( x + 1 - \frac { 3 } { 5 - 1 } ) \cdot \frac { x - 1 } { x - 2 }$$

Evaluate

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

Short Solution Steps

Subtract 1 from 5 to get 4.

$$1\left(x+1-\frac{3}{4}\right)\times \frac{x-1}{x-2}$$

Convert 1 to fraction \frac{4}{4}.

$$1\left(x+\frac{4}{4}-\frac{3}{4}\right)\times \frac{x-1}{x-2}$$

Since \frac{4}{4} and \frac{3}{4} have the same denominator, subtract them by subtracting their numerators.

$$1\left(x+\frac{4-3}{4}\right)\times \frac{x-1}{x-2}$$

Subtract 3 from 4 to get 1.

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

Express 1\times \frac{x-1}{x-2} as a single fraction.

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

Use the distributive property to multiply \frac{x-1}{x-2} by x+\frac{1}{4}.

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

Express \frac{x-1}{x-2}x as a single fraction.

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

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

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-2 and \left(x-2\right)\times 4 is 4\left(x-2\right). Multiply \frac{\left(x-1\right)x}{x-2} times \frac{4}{4}.

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

Since \frac{4\left(x-1\right)x}{4\left(x-2\right)} and \frac{x-1}{4\left(x-2\right)} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 4\left(x-1\right)x+x-1.

$$\frac{4x^{2}-4x+x-1}{4\left(x-2\right)}$$

Combine like terms in 4x^{2}-4x+x-1.

$$\frac{4x^{2}-3x-1}{4\left(x-2\right)}$$

Expand 4\left(x-2\right).

$$\frac{4x^{2}-3x-1}{4x-8}$$

Expand

$$\frac{4x^{2}-3x-1}{4\left(x-2\right)}$$

Short Solution Steps

Subtract 1 from 5 to get 4.

$$1\left(x+1-\frac{3}{4}\right)\times \frac{x-1}{x-2}$$

Convert 1 to fraction \frac{4}{4}.

$$1\left(x+\frac{4}{4}-\frac{3}{4}\right)\times \frac{x-1}{x-2}$$

Since \frac{4}{4} and \frac{3}{4} have the same denominator, subtract them by subtracting their numerators.

$$1\left(x+\frac{4-3}{4}\right)\times \frac{x-1}{x-2}$$

Subtract 3 from 4 to get 1.

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

Express 1\times \frac{x-1}{x-2} as a single fraction.

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

Use the distributive property to multiply \frac{x-1}{x-2} by x+\frac{1}{4}.

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

Express \frac{x-1}{x-2}x as a single fraction.

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

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

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-2 and \left(x-2\right)\times 4 is 4\left(x-2\right). Multiply \frac{\left(x-1\right)x}{x-2} times \frac{4}{4}.

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

Since \frac{4\left(x-1\right)x}{4\left(x-2\right)} and \frac{x-1}{4\left(x-2\right)} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 4\left(x-1\right)x+x-1.

$$\frac{4x^{2}-4x+x-1}{4\left(x-2\right)}$$

Combine like terms in 4x^{2}-4x+x-1.

$$\frac{4x^{2}-3x-1}{4\left(x-2\right)}$$

Expand 4\left(x-2\right).

$$\frac{4x^{2}-3x-1}{4x-8}$$