Solve ax/x+y+ay/x+y

$$\frac { a x } { x + y } + \frac { a y } { x + y }$$

Evaluate

$$a$$

Short Solution Steps

Since \frac{ax}{x+y} and \frac{ay}{x+y} have the same denominator, add them by adding their numerators.

$$\frac{ax+ay}{x+y}$$

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

$$\frac{a\left(x+y\right)}{x+y}$$

Cancel out x+y in both numerator and denominator.

$$a$$

Differentiate w.r.t. a

$$1$$

Steps Using Definition of a Derivative

Since \frac{ax}{x+y} and \frac{ay}{x+y} have the same denominator, add them by adding their numerators.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{ax+ay}{x+y})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a\left(x+y\right)}{x+y})$$

Cancel out x+y in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a)$$

The derivative of ax^{n} is nax^{n-1}.

$$a^{1-1}$$

Subtract 1 from 1.

$$a^{0}$$

For any term t except 0, t^{0}=1.

$$1$$