Solve u+a+7u/u+a

$$u + a + \frac { 7 u } { u + a }$$

Evaluate

$$\frac{u^{2}+2au+7u+a^{2}}{u+a}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply u+a times \frac{u+a}{u+a}.

$$\frac{\left(u+a\right)\left(u+a\right)}{u+a}+\frac{7u}{u+a}$$

Since \frac{\left(u+a\right)\left(u+a\right)}{u+a} and \frac{7u}{u+a} have the same denominator, add them by adding their numerators.

$$\frac{\left(u+a\right)\left(u+a\right)+7u}{u+a}$$

Do the multiplications in \left(u+a\right)\left(u+a\right)+7u.

$$\frac{u^{2}+ua+ua+a^{2}+7u}{u+a}$$

Combine like terms in u^{2}+ua+ua+a^{2}+7u.

$$\frac{u^{2}+a^{2}+2ua+7u}{u+a}$$

Differentiate w.r.t. a

$$\frac{u^{2}+2au-7u+a^{2}}{\left(u+a\right)^{2}}$$