Solve 9a/5a-5-a-9/a-1=

$$\frac { 9 a } { 5 a - 5 } - \frac { a - 9 } { a - 1 } =$$

Evaluate

$$\frac{4a+45}{5\left(a-1\right)}$$

Short Solution Steps

Factor 5a-5.

$$\frac{9a}{5\left(a-1\right)}-\frac{a-9}{a-1}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5\left(a-1\right) and a-1 is 5\left(a-1\right). Multiply \frac{a-9}{a-1} times \frac{5}{5}.

$$\frac{9a}{5\left(a-1\right)}-\frac{5\left(a-9\right)}{5\left(a-1\right)}$$

Since \frac{9a}{5\left(a-1\right)} and \frac{5\left(a-9\right)}{5\left(a-1\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9a-5\left(a-9\right)}{5\left(a-1\right)}$$

Do the multiplications in 9a-5\left(a-9\right).

$$\frac{9a-5a+45}{5\left(a-1\right)}$$

Combine like terms in 9a-5a+45.

$$\frac{4a+45}{5\left(a-1\right)}$$

Expand 5\left(a-1\right).

$$\frac{4a+45}{5a-5}$$

Expand

$$\frac{4a+45}{5\left(a-1\right)}$$

Short Solution Steps

Factor 5a-5.

$$\frac{9a}{5\left(a-1\right)}-\frac{a-9}{a-1}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5\left(a-1\right) and a-1 is 5\left(a-1\right). Multiply \frac{a-9}{a-1} times \frac{5}{5}.

$$\frac{9a}{5\left(a-1\right)}-\frac{5\left(a-9\right)}{5\left(a-1\right)}$$

Since \frac{9a}{5\left(a-1\right)} and \frac{5\left(a-9\right)}{5\left(a-1\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9a-5\left(a-9\right)}{5\left(a-1\right)}$$

Do the multiplications in 9a-5\left(a-9\right).

$$\frac{9a-5a+45}{5\left(a-1\right)}$$

Combine like terms in 9a-5a+45.

$$\frac{4a+45}{5\left(a-1\right)}$$

Expand 5\left(a-1\right).

$$\frac{4a+45}{5a-5}$$