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

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

Evaluate

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

Short Solution Steps

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

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

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

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

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

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

Combine like terms in 2b+4+3a-3.

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

Expand \left(a-1\right)\left(b+2\right).

$$\frac{2b+1+3a}{ab+2a-b-2}$$

Differentiate w.r.t. b

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