Solve 1a-1/a^2-3a-28+6/a+4

$$\frac { 1 a - 1 } { a ^ { 2 } - 3 a - 28 } + \frac { 6 } { a + 4 }$$

Evaluate

$$\frac{7a-43}{\left(a-7\right)\left(a+4\right)}$$

Short Solution Steps

Factor a^{2}-3a-28.

$$\frac{1a-1}{\left(a-7\right)\left(a+4\right)}+\frac{6}{a+4}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(a-7\right)\left(a+4\right) and a+4 is \left(a-7\right)\left(a+4\right). Multiply \frac{6}{a+4} times \frac{a-7}{a-7}.

$$\frac{1a-1}{\left(a-7\right)\left(a+4\right)}+\frac{6\left(a-7\right)}{\left(a-7\right)\left(a+4\right)}$$

Since \frac{1a-1}{\left(a-7\right)\left(a+4\right)} and \frac{6\left(a-7\right)}{\left(a-7\right)\left(a+4\right)} have the same denominator, add them by adding their numerators.

$$\frac{1a-1+6\left(a-7\right)}{\left(a-7\right)\left(a+4\right)}$$

Do the multiplications in 1a-1+6\left(a-7\right).

$$\frac{a-1+6a-42}{\left(a-7\right)\left(a+4\right)}$$

Combine like terms in a-1+6a-42.

$$\frac{7a-43}{\left(a-7\right)\left(a+4\right)}$$

Expand \left(a-7\right)\left(a+4\right).

$$\frac{7a-43}{a^{2}-3a-28}$$

Expand

$$\frac{7a-43}{\left(a-7\right)\left(a+4\right)}$$

Short Solution Steps

Factor a^{2}-3a-28.

$$\frac{1a-1}{\left(a-7\right)\left(a+4\right)}+\frac{6}{a+4}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(a-7\right)\left(a+4\right) and a+4 is \left(a-7\right)\left(a+4\right). Multiply \frac{6}{a+4} times \frac{a-7}{a-7}.

$$\frac{1a-1}{\left(a-7\right)\left(a+4\right)}+\frac{6\left(a-7\right)}{\left(a-7\right)\left(a+4\right)}$$

Since \frac{1a-1}{\left(a-7\right)\left(a+4\right)} and \frac{6\left(a-7\right)}{\left(a-7\right)\left(a+4\right)} have the same denominator, add them by adding their numerators.

$$\frac{1a-1+6\left(a-7\right)}{\left(a-7\right)\left(a+4\right)}$$

Do the multiplications in 1a-1+6\left(a-7\right).

$$\frac{a-1+6a-42}{\left(a-7\right)\left(a+4\right)}$$

Combine like terms in a-1+6a-42.

$$\frac{7a-43}{\left(a-7\right)\left(a+4\right)}$$

Expand \left(a-7\right)\left(a+4\right).

$$\frac{7a-43}{a^{2}-3a-28}$$