Solve a/6a-36-a-5/a-6=

$$\frac { a } { 6 a - 36 } - \frac { a - 5 } { a - 6 } =$$

Evaluate

$$-\frac{5}{6}\approx -0.833333333$$

Short Solution Steps

Factor 6a-36.

$$\frac{a}{6\left(a-6\right)}-\frac{a-5}{a-6}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 6\left(a-6\right) and a-6 is 6\left(a-6\right). Multiply \frac{a-5}{a-6} times \frac{6}{6}.

$$\frac{a}{6\left(a-6\right)}-\frac{6\left(a-5\right)}{6\left(a-6\right)}$$

Since \frac{a}{6\left(a-6\right)} and \frac{6\left(a-5\right)}{6\left(a-6\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{a-6\left(a-5\right)}{6\left(a-6\right)}$$

Do the multiplications in a-6\left(a-5\right).

$$\frac{a-6a+30}{6\left(a-6\right)}$$

Combine like terms in a-6a+30.

$$\frac{-5a+30}{6\left(a-6\right)}$$

Factor the expressions that are not already factored in \frac{-5a+30}{6\left(a-6\right)}.

$$\frac{5\left(-a+6\right)}{6\left(a-6\right)}$$

Extract the negative sign in 6-a.

$$\frac{-5\left(a-6\right)}{6\left(a-6\right)}$$

Cancel out a-6 in both numerator and denominator.

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

Fraction \frac{-5}{6} can be rewritten as -\frac{5}{6} by extracting the negative sign.

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

Factor

$$-\frac{5}{6} = -0.8333333333333334$$