Solve 2b/b+1+3/b-5

$$\frac { 2 b } { b + 1 } + \frac { 3 } { b - 5 }$$

Evaluate

$$\frac{\left(b-3\right)\left(2b-1\right)}{\left(b-5\right)\left(b+1\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of b+1 and b-5 is \left(b-5\right)\left(b+1\right). Multiply \frac{2b}{b+1} times \frac{b-5}{b-5}. Multiply \frac{3}{b-5} times \frac{b+1}{b+1}.

$$\frac{2b\left(b-5\right)}{\left(b-5\right)\left(b+1\right)}+\frac{3\left(b+1\right)}{\left(b-5\right)\left(b+1\right)}$$

Since \frac{2b\left(b-5\right)}{\left(b-5\right)\left(b+1\right)} and \frac{3\left(b+1\right)}{\left(b-5\right)\left(b+1\right)} have the same denominator, add them by adding their numerators.

$$\frac{2b\left(b-5\right)+3\left(b+1\right)}{\left(b-5\right)\left(b+1\right)}$$

Do the multiplications in 2b\left(b-5\right)+3\left(b+1\right).

$$\frac{2b^{2}-10b+3b+3}{\left(b-5\right)\left(b+1\right)}$$

Combine like terms in 2b^{2}-10b+3b+3.

$$\frac{2b^{2}-7b+3}{\left(b-5\right)\left(b+1\right)}$$

Expand \left(b-5\right)\left(b+1\right).

$$\frac{2b^{2}-7b+3}{b^{2}-4b-5}$$

Differentiate w.r.t. b

$$\frac{47-26b-b^{2}}{b^{4}-8b^{3}+6b^{2}+40b+25}$$