Solve 5/a-3/a+b

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

Evaluate

$$\frac{2a+5b}{a\left(a+b\right)}$$

Short Solution Steps

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

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

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

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

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

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

Combine like terms in 5a+5b-3a.

$$\frac{2a+5b}{a\left(a+b\right)}$$

Expand a\left(a+b\right).

$$\frac{2a+5b}{a^{2}+ab}$$

Differentiate w.r.t. a

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