Solve 2/b-7+b+6/b^2-b-42

$$\frac { 2 } { b - 7 } + \frac { b + 6 } { b ^ { 2 } - b - 42 }$$

Evaluate

$$\frac{3}{b-7}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{b+6}{b^{2}-b-42}.

$$\frac{2}{b-7}+\frac{b+6}{\left(b-7\right)\left(b+6\right)}$$

Cancel out b+6 in both numerator and denominator.

$$\frac{2}{b-7}+\frac{1}{b-7}$$

Since \frac{2}{b-7} and \frac{1}{b-7} have the same denominator, add them by adding their numerators. Add 2 and 1 to get 3.

$$\frac{3}{b-7}$$

Expand

$$\frac{3}{b-7}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{b+6}{b^{2}-b-42}.

$$\frac{2}{b-7}+\frac{b+6}{\left(b-7\right)\left(b+6\right)}$$

Cancel out b+6 in both numerator and denominator.

$$\frac{2}{b-7}+\frac{1}{b-7}$$

Since \frac{2}{b-7} and \frac{1}{b-7} have the same denominator, add them by adding their numerators. Add 2 and 1 to get 3.

$$\frac{3}{b-7}$$