Solve 5/u+frac{26{u}-10}+1

$$\frac { 5 } { u + \frac { 26 } { u } - 10 } + 1$$

Evaluate

$$\frac{u^{2}-5u+26}{u^{2}-10u+26}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply u-10 times \frac{u}{u}.

$$\frac{5}{\frac{\left(u-10\right)u}{u}+\frac{26}{u}}+1$$

Since \frac{\left(u-10\right)u}{u} and \frac{26}{u} have the same denominator, add them by adding their numerators.

$$\frac{5}{\frac{\left(u-10\right)u+26}{u}}+1$$

Do the multiplications in \left(u-10\right)u+26.

$$\frac{5}{\frac{u^{2}-10u+26}{u}}+1$$

Divide 5 by \frac{u^{2}-10u+26}{u} by multiplying 5 by the reciprocal of \frac{u^{2}-10u+26}{u}.

$$\frac{5u}{u^{2}-10u+26}+1$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{u^{2}-10u+26}{u^{2}-10u+26}.

$$\frac{5u}{u^{2}-10u+26}+\frac{u^{2}-10u+26}{u^{2}-10u+26}$$

Since \frac{5u}{u^{2}-10u+26} and \frac{u^{2}-10u+26}{u^{2}-10u+26} have the same denominator, add them by adding their numerators.

$$\frac{5u+u^{2}-10u+26}{u^{2}-10u+26}$$

Combine like terms in 5u+u^{2}-10u+26.

$$\frac{-5u+u^{2}+26}{u^{2}-10u+26}$$

Differentiate w.r.t. u

$$\frac{5\left(26-u^{2}\right)}{\left(u^{2}-10u+26\right)^{2}}$$