Solve 5/5a-5-5/3a-6

$$\frac { 5 } { 5 a - 5 } - \frac { 5 } { 3 a - 6 }$$

Evaluate

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

Short Solution Steps

Factor 5a-5. Factor 3a-6.

$$\frac{5}{5\left(a-1\right)}-\frac{5}{3\left(a-2\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5\left(a-1\right) and 3\left(a-2\right) is 15\left(a-2\right)\left(a-1\right). Multiply \frac{5}{5\left(a-1\right)} times \frac{3\left(a-2\right)}{3\left(a-2\right)}. Multiply \frac{5}{3\left(a-2\right)} times \frac{5\left(a-1\right)}{5\left(a-1\right)}.

$$\frac{5\times 3\left(a-2\right)}{15\left(a-2\right)\left(a-1\right)}-\frac{5\times 5\left(a-1\right)}{15\left(a-2\right)\left(a-1\right)}$$

Since \frac{5\times 3\left(a-2\right)}{15\left(a-2\right)\left(a-1\right)} and \frac{5\times 5\left(a-1\right)}{15\left(a-2\right)\left(a-1\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5\times 3\left(a-2\right)-5\times 5\left(a-1\right)}{15\left(a-2\right)\left(a-1\right)}$$

Do the multiplications in 5\times 3\left(a-2\right)-5\times 5\left(a-1\right).

$$\frac{15a-30-25a+25}{15\left(a-2\right)\left(a-1\right)}$$

Combine like terms in 15a-30-25a+25.

$$\frac{-10a-5}{15\left(a-2\right)\left(a-1\right)}$$

Factor the expressions that are not already factored in \frac{-10a-5}{15\left(a-2\right)\left(a-1\right)}.

$$\frac{5\left(-2a-1\right)}{15\left(a-2\right)\left(a-1\right)}$$

Cancel out 5 in both numerator and denominator.

$$\frac{-2a-1}{3\left(a-2\right)\left(a-1\right)}$$

Expand 3\left(a-2\right)\left(a-1\right).

$$\frac{-2a-1}{3a^{2}-9a+6}$$

Factor

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