Solve a-a+5/a-3/a+1

$$\frac { a - \frac { a + 5 } { a - 3 } } { a + 1 }$$

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply a times \frac{a-3}{a-3}.

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

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

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

Do the multiplications in a\left(a-3\right)-\left(a+5\right).

$$\frac{\frac{a^{2}-3a-a-5}{a-3}}{a+1}$$

Combine like terms in a^{2}-3a-a-5.

$$\frac{\frac{a^{2}-4a-5}{a-3}}{a+1}$$

Express \frac{\frac{a^{2}-4a-5}{a-3}}{a+1} as a single fraction.

$$\frac{a^{2}-4a-5}{\left(a-3\right)\left(a+1\right)}$$

Factor the expressions that are not already factored.

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

Cancel out a+1 in both numerator and denominator.

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

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply a times \frac{a-3}{a-3}.

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

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

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

Do the multiplications in a\left(a-3\right)-\left(a+5\right).

$$\frac{\frac{a^{2}-3a-a-5}{a-3}}{a+1}$$

Combine like terms in a^{2}-3a-a-5.

$$\frac{\frac{a^{2}-4a-5}{a-3}}{a+1}$$

Express \frac{\frac{a^{2}-4a-5}{a-3}}{a+1} as a single fraction.

$$\frac{a^{2}-4a-5}{\left(a-3\right)\left(a+1\right)}$$

Factor the expressions that are not already factored.

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

Cancel out a+1 in both numerator and denominator.

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