Solve 2x/ax+bx+3y/ay+by

$$\frac { 2 x } { a x + b x } + \frac { 3 y } { a y + b y }$$

Evaluate

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{2x}{ax+bx}.

$$\frac{2x}{x\left(a+b\right)}+\frac{3y}{ay+by}$$

Cancel out x in both numerator and denominator.

$$\frac{2}{a+b}+\frac{3y}{ay+by}$$

Factor the expressions that are not already factored in \frac{3y}{ay+by}.

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

Cancel out y in both numerator and denominator.

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

Since \frac{2}{a+b} and \frac{3}{a+b} have the same denominator, add them by adding their numerators. Add 2 and 3 to get 5.

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

Differentiate w.r.t. a

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