Solve 3b-1/b-4-2+b/b^2-4b=

$$\frac { 3 b - 1 } { b - 4 } - \frac { 2 + b } { b ^ { 2 } - 4 b } =$$

Evaluate

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

Short Solution Steps

Factor b^{2}-4b.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of b-4 and b\left(b-4\right) is b\left(b-4\right). Multiply \frac{3b-1}{b-4} times \frac{b}{b}.

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

Since \frac{\left(3b-1\right)b}{b\left(b-4\right)} and \frac{2+b}{b\left(b-4\right)} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in \left(3b-1\right)b-\left(2+b\right).

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

Combine like terms in 3b^{2}-b-2-b.

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

Expand b\left(b-4\right).

$$\frac{3b^{2}-2b-2}{b^{2}-4b}$$

Expand

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

Short Solution Steps

Factor b^{2}-4b.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of b-4 and b\left(b-4\right) is b\left(b-4\right). Multiply \frac{3b-1}{b-4} times \frac{b}{b}.

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

Since \frac{\left(3b-1\right)b}{b\left(b-4\right)} and \frac{2+b}{b\left(b-4\right)} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in \left(3b-1\right)b-\left(2+b\right).

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

Combine like terms in 3b^{2}-b-2-b.

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

Expand b\left(b-4\right).

$$\frac{3b^{2}-2b-2}{b^{2}-4b}$$